Description of problem:
The monitors of the Ghia mini-pc get misconfigured every time. The result is: you don't see the login screen and, the main monitor, get's detected as the second one.

Check this out:
$ xrandr -q
Screen 0: minimum 320 x 200, current 1680 x 1050, maximum 4096 x 4096
LVDS1 connected (normal left inverted right x axis y axis)
   1024x768       60.0 +
   800x600        60.3     56.2  
   640x480        59.9  
VGA1 connected 1680x1050+0+0 (normal left inverted right x axis y axis) 473mm x 296mm
   1680x1050      60.0*+
   1600x1000      60.0  
   1280x1024      75.0  
   1440x900       59.9  
   1280x960       60.0  
   1152x864       75.0  
   1152x720       60.0  
   1024x768       75.1     60.0  
   832x624        74.6  
   800x600        75.0     60.3  
   640x480        75.0     60.0  
   720x400        70.1 

The thing is that LVDS1 does not have a physical connection... it doesn't exist.

My guess is that the MB is used for netbooks too. Anyway, I solved this by creating the /etc/gnome-settings-daemon/xrandr/monitors.xml 

with the following contents:
<monitors version="1">
  <configuration>
      <clone>no</clone>
      <output name="default">
          <vendor>???</vendor>
          <product>0x0000</product>
          <serial>0x00000000</serial>
          <width>1024</width>
          <height>768</height>
          <rate>0</rate>
          <x>0</x>
          <y>0</y>
          <rotation>normal</rotation>
          <reflect_x>no</reflect_x>
          <reflect_y>no</reflect_y>
          <primary>yes</primary>
      </output>
  </configuration>
  <configuration>
      <clone>no</clone>
      <output name="LVDS1">
          <vendor>???</vendor>
          <product>0x0000</product>
          <serial>0x00000000</serial>
          <primary>no</primary>
      </output>
      <output name="VGA1">
          <vendor>HWP</vendor>
          <product>0x26a8</product>
          <serial>0x01010101</serial>
          <width>1680</width>
          <height>1050</height>
          <rate>60</rate>
          <x>0</x>
          <y>0</y>
          <rotation>normal</rotation>
          <reflect_x>no</reflect_x>
          <reflect_y>no</reflect_y>
          <primary>yes</primary>
      </output>
  </configuration>
</monitors>

As much as I played with gsettings, I couldn't make the changes. Also, while playing with xrandr, I found that:

DISPLAY=:0 xrandr --output LVDS1 --off --output VGA1 --primary

resolved the issue but did not persist. So, the above solution worked.

Anyway, I hope this gets worked out. I've seen enough posts about this; with inconsistent solutions.