You can close the bug report now. Apprently a simple reboot, I did reboot the machine after the update, did "fix" the problem. Strange.

ok

Actually, I just realized this is a bug and it is related to SELinux. I forgot that I changed the SELinux to permissive mode before my last reboot. The problem came back after I changed to enforcing mode again.
I tried to "audit2allow -alr" in the permissive mode and what came up seems unrelated to NetworkManager which seems strange to me. I have the output pasted below any way.
Please let me know how I can test this for you to further trouble shooting. 
-bash-4.2# audit2allow -alr

require {
	type init_t;
	type initrc_t;
	type colord_t;
	type cupsd_t;
	class dbus send_msg;
}

#============= colord_t ==============
allow colord_t initrc_t:dbus send_msg;

#============= cupsd_t ==============
allow cupsd_t init_t:dbus send_msg;

What AVCs are you seeing?

Try a VPN connection and search for the AVC:
# ausearch -m avc -ts today

I tried in "permissive" mode and I didn't get anything from the ausearch, even after I connected to VPN successfully. 
I know this may sound weird, however the only difference I changed to make the system working is set to "permissive" mode and reboot. 
The following is the test I just did, outputs with comments.
###  System booted in "enforcing" mode
[awang@mars ~]$ sudo su -
-bash-4.2# getenforce
Enforcing
-bash-4.2# systemctl status NetworkManager.service
NetworkManager.service - Network Manager
	  Loaded: loaded (/lib/systemd/system/NetworkManager.service; enabled)
	  Active: active (running) since Mon, 04 Jun 2012 15:36:07 -0700; 1min 13s ago
	Main PID: 1089 (NetworkManager)
	  CGroup: name=systemd:/system/NetworkManager.service
		  ├ 1089 /usr/sbin/NetworkManager --no-daemon
		  └ 1500 /sbin/dhclient -d -4 -sf /usr/libexec/nm-dhcp-clie...

### The NetworkManager is running, however I can't see its icon in notification area
### As shown in the top half of the attached screen shot, error.jpg
-bash-4.2# systemctl restart NetworkManager.service
-bash-4.2# systemctl status NetworkManager.service
NetworkManager.service - Network Manager
	  Loaded: loaded (/lib/systemd/system/NetworkManager.service; enabled)
	  Active: active (running) since Mon, 04 Jun 2012 15:37:37 -0700; 6s ago
	Main PID: 2601 (NetworkManager)
	  CGroup: name=systemd:/system/NetworkManager.service
		  ├ 2601 /usr/sbin/NetworkManager --no-daemon
		  └ 2611 /sbin/dhclient -d -4 -sf /usr/libexec/nm-dhcp-clie...

### Restart the NetworkManager would make the icon appear in the notification area.
### As shown in the bottom half of the screen shot, error.jpg.
### However the VPN still wouldn't work. 
-bash-4.2# tail -f /var/log/messages
Jun  4 15:37:38 mars abrtd: DUP_OF_DIR: /var/spool/abrt/ccpp-2012-06-04-15:34:44-2303
Jun  4 15:37:38 mars abrtd: Problem directory is a duplicate of /var/spool/abrt/ccpp-2012-06-04-15:34:44-2303
Jun  4 15:37:38 mars abrtd: Deleting problem directory ccpp-2012-06-04-15:37:37-2309 (dup of ccpp-2012-06-04-15:34:44-2303)
Jun  4 15:37:39 mars avahi-daemon[1849]: Registering new address record for fe80::16da:e9ff:fef5:4699 on p6p1.*.
Jun  4 15:37:39 mars dnsmasq[1304]: reading /etc/resolv.conf
Jun  4 15:37:39 mars dnsmasq[1304]: using nameserver 192.168.254.1#53
Jun  4 15:37:57 mars NetworkManager[2601]: <info> (p6p1): IP6 addrconf timed out or failed.
Jun  4 15:37:57 mars NetworkManager[2601]: <info> Activation (p6p1) Stage 4 of 5 (IPv6 Configure Timeout) scheduled...
Jun  4 15:37:57 mars NetworkManager[2601]: <info> Activation (p6p1) Stage 4 of 5 (IPv6 Configure Timeout) started...
Jun  4 15:37:57 mars NetworkManager[2601]: <info> Activation (p6p1) Stage 4 of 5 (IPv6 Configure Timeout) complete.
Jun  4 15:40:08 mars NetworkManager[2601]: <info> Starting VPN service 'openconnect'...
Jun  4 15:40:09 mars NetworkManager[2601]: <info> VPN service 'openconnect' started (org.freedesktop.NetworkManager.openconnect), PID 2824
Jun  4 15:40:09 mars NetworkManager[2601]: <info> VPN service 'openconnect' appeared; activating connections
Jun  4 15:40:09 mars NetworkManager[2601]: <info> VPN plugin state changed: init (1)
Jun  4 15:40:09 mars NetworkManager[2601]: <warn> /sys/devices/virtual/net/vpn0: couldn't determine device driver; ignoring...
Jun  4 15:40:09 mars NetworkManager[2601]: <error> [1338849609.55797] [nm-vpn-connection.c:934] get_secrets_cb(): Failed to request VPN secrets #2: (6) No agents were available for this request.
Jun  4 15:40:09 mars NetworkManager[2601]: <info> Policy set 'Wired connection 1' (p6p1) as default for IPv4 routing and DNS.
Jun  4 15:40:14 mars avahi-daemon[1849]: Withdrawing workstation service for vpn0.
Jun  4 15:40:14 mars NetworkManager[2601]: <info> VPN service 'openconnect' disappeared
^C

### Manually set it to "permissive" mode wouldn't help.
-bash-4.2# setenforce 0
-bash-4.2# systemctl restart NetworkManager.service
-bash-4.2# systemctl status NetworkManager.service
NetworkManager.service - Network Manager
	  Loaded: loaded (/lib/systemd/system/NetworkManager.service; enabled)
	  Active: active (running) since Mon, 04 Jun 2012 15:41:26 -0700; 8s ago
	Main PID: 2865 (NetworkManager)
	  CGroup: name=systemd:/system/NetworkManager.service
		  ├ 2865 /usr/sbin/NetworkManager --no-daemon
		  └ 2873 /sbin/dhclient -d -4 -sf /usr/libexec/nm-dhcp-clie...
-bash-4.2# tail -f /var/log/messages
......
Jun  4 15:41:46 mars NetworkManager[2865]: <info> (p6p1): IP6 addrconf timed out or failed.
Jun  4 15:41:46 mars NetworkManager[2865]: <info> Activation (p6p1) Stage 4 of 5 (IPv6 Configure Timeout) scheduled...
Jun  4 15:41:46 mars NetworkManager[2865]: <info> Activation (p6p1) Stage 4 of 5 (IPv6 Configure Timeout) started...
Jun  4 15:41:46 mars NetworkManager[2865]: <info> Activation (p6p1) Stage 4 of 5 (IPv6 Configure Timeout) complete.
Jun  4 15:42:00 mars NetworkManager[2865]: <info> Starting VPN service 'openconnect'...
Jun  4 15:42:00 mars NetworkManager[2865]: <info> VPN service 'openconnect' started (org.freedesktop.NetworkManager.openconnect), PID 3015
Jun  4 15:42:00 mars NetworkManager[2865]: <info> VPN service 'openconnect' appeared; activating connections
Jun  4 15:42:00 mars NetworkManager[2865]: <info> VPN plugin state changed: init (1)
Jun  4 15:42:00 mars NetworkManager[2865]: <warn> /sys/devices/virtual/net/vpn0: couldn't determine device driver; ignoring...
Jun  4 15:42:00 mars NetworkManager[2865]: <error> [1338849720.986549] [nm-vpn-connection.c:934] get_secrets_cb(): Failed to request VPN secrets #2: (6) No agents were available for this request.
Jun  4 15:42:00 mars NetworkManager[2865]: <info> Policy set 'Wired connection 1' (p6p1) as default for IPv4 routing and DNS.
Jun  4 15:42:05 mars avahi-daemon[1849]: Withdrawing workstation service for vpn0.
Jun  4 15:42:05 mars NetworkManager[2865]: <info> VPN service 'openconnect' disappeared
^C
-bash-4.2# 

### Reboot the machine in "permissive" mode and everything starts to work again.
[awang@mars ~]$ sudo su -
-bash-4.2# getenforce
Permissive
-bash-4.2# tail -f /var/log/messages
.......
Jun  4 15:44:58 mars NetworkManager[1081]: <info> Starting VPN service 'openconnect'...
Jun  4 15:44:58 mars NetworkManager[1081]: <info> VPN service 'openconnect' started (org.freedesktop.NetworkManager.openconnect), PID 2158
Jun  4 15:44:58 mars NetworkManager[1081]: <info> VPN service 'openconnect' appeared; activating connections
Jun  4 15:44:58 mars NetworkManager[1081]: <warn> /sys/devices/virtual/net/vpn0: couldn't determine device driver; ignoring...
Jun  4 15:45:03 mars NetworkManager[1081]: <info> VPN plugin state changed: starting (3)
Jun  4 15:45:03 mars NetworkManager[1081]: <info> VPN connection 'ALF' (Connect) reply received.
Jun  4 15:45:03 mars openconnect[2167]: Attempting to connect to 206.113.209.252:443
Jun  4 15:45:03 mars openconnect[2167]: SSL negotiation with vpn-alf.inovis.com
Jun  4 15:45:04 mars openconnect[2167]: Connected to HTTPS on vpn-alf.inovis.com
Jun  4 15:45:04 mars openconnect[2167]: Got CONNECT response: HTTP/1.1 200 OK
Jun  4 15:45:04 mars openconnect[2167]: CSTP connected. DPD 30, Keepalive 20
Jun  4 15:45:04 mars NetworkManager[1081]: <info> VPN connection 'ALF' (IP Config Get) reply received.
Jun  4 15:45:04 mars NetworkManager[1081]: <info> VPN Gateway: 206.113.209.252
Jun  4 15:45:04 mars NetworkManager[1081]: <info> Tunnel Device: vpn0
Jun  4 15:45:04 mars NetworkManager[1081]: <info> Internal IP4 Address: 10.32.202.20
Jun  4 15:45:04 mars NetworkManager[1081]: <info> Internal IP4 Prefix: 24
Jun  4 15:45:04 mars NetworkManager[1081]: <info> Internal IP4 Point-to-Point Address: 10.32.202.20
Jun  4 15:45:04 mars NetworkManager[1081]: <info> Maximum Segment Size (MSS): 0
Jun  4 15:45:04 mars NetworkManager[1081]: <info> Forbid Default Route: no
Jun  4 15:45:04 mars NetworkManager[1081]: <info> Internal IP4 DNS: 10.32.1.20
Jun  4 15:45:04 mars NetworkManager[1081]: <info> Internal IP4 DNS: 10.32.1.21
Jun  4 15:45:04 mars NetworkManager[1081]: <info> DNS Domain: 'itlogon.com'
Jun  4 15:45:04 mars openconnect[2167]: Connected vpn0 as 10.32.202.20, using SSL + deflate
Jun  4 15:45:04 mars dnsmasq[1286]: reading /etc/resolv.conf
Jun  4 15:45:04 mars dnsmasq[1286]: using nameserver 192.168.254.1#53
Jun  4 15:45:04 mars openconnect[2167]: Established DTLS connection
Jun  4 15:45:05 mars NetworkManager[1081]: <info> VPN connection 'ALF' (IP Config Get) complete.
Jun  4 15:45:05 mars NetworkManager[1081]: <info> Policy set 'ALF' (vpn0) as default for IPv4 routing and DNS.
Jun  4 15:45:05 mars NetworkManager[1081]: <info> VPN plugin state changed: started (4)
Jun  4 15:45:05 mars dbus[1120]: [system] Activating service name='org.freedesktop.nm_dispatcher' (using servicehelper)
Jun  4 15:45:05 mars NetworkManager[1081]:    keyfile: updating /etc/NetworkManager/system-connections/ALF
Jun  4 15:45:05 mars dbus-daemon[1120]: dbus[1120]: [system] Activating service name='org.freedesktop.nm_dispatcher' (using servicehelper)
Jun  4 15:45:05 mars dbus[1120]: [system] Successfully activated service 'org.freedesktop.nm_dispatcher'
Jun  4 15:45:05 mars dbus-daemon[1120]: dbus[1120]: [system] Successfully activated service 'org.freedesktop.nm_dispatcher'
Jun  4 15:45:07 mars chronyd[1115]: Selected source 65.23.154.62
^C

### There is no AVC messages. 
-bash-4.2# 
-bash-4.2# ausearch -m avc -ts today
<no matches>
-bash-4.2# 

### I have no reason to believe these are related to the problem I'm dealing with.
-bash-4.2# audit2allow -alr

require {
	type init_t;
	type initrc_t;
	type colord_t;
	type cupsd_t;
	class dbus send_msg;
}

#============= colord_t ==============
allow colord_t initrc_t:dbus send_msg;

#============= cupsd_t ==============
allow cupsd_t init_t:dbus send_msg;

Created attachment 589288 [details]
screen shot of notification area.

*** This bug has been marked as a duplicate of bug 826706 ***