When I try to start X with "startx", I get the following error log:

----- Begin Log -----
Fatal server error:
Cannot open log file "/var/log/XFree86.0.log"


When reporting a problem related to a server crash, please send
the full server output, not just the last messages.
This can be found in the log file "/var/log/XFree86.0.log".

giving up.
xinit:  Connection refused (errno 111):  unable to connect to X server
xinit:  No such process (errno 3):  Server error.
----- End Log -----

There's at least one obvious problem to me.  It's trying to write an error
log into /var/log and I, as an ordinary user, am not allowed to do that.  I
am not sure if that's the only problem, though.