Desktop locked up. Hard poweroff. Now gdm starts but x session can't

Try to press CTRL+ALT+F2 a login terminal must appear, make a login with your user and password and then try to restart gdm by typing:
sudo /etc/init.d/gdm restart

Post error here.

HTH

That didn't work. gdm starts, I login and get the message can't start session ...click ok and it puts me in an xterm. X is running, I have a functioning mouse cursor, so it's not X it's something about my last session not exiting cleanly. What is left behind when an x session is closed abruptly by power going off?

Try to press CTRL+ALT+F2 a login terminal must appear, make a login with your user and password and then try to restart gdm by typing:
startx
Pls keep us informed,
br,
Bhavani Shankar.

Check (or copy here) some logs:
/var/log/gdm/:0.log
/var/log/Xorg.0.log

Nothing in :0.log or Xorg.0.log but there is something in my home directory in .xsession-errors. It reports when it runs /etc/gdm/Xsession it's connection to xserver was refused. So it's not a login problem and xorg is running. Any more ideas?

Such error:
Xlib: connection to ":0.0" refused by server
Xlib: No protocol specified

xhost: unable to open display ":0.0"
?

Many things can be left over depending on the programs running, most in /tmp, some things are saved in different hidden directories in your home folder also.

By the way, if your desktop locks it's often still possible to soft boot using kernel magic, that is hold Alt+SysRq and press R E I S U B (http://www.mjmwired.net/kernel/Documentation/sysrq.txt). Or if it's not so very locked using another tty, Alt+Ctrl+FX, login, sudo reboot now.

An idea: make a new user with "adduser" and try using this new account.

yes it might work out with magic-sysrq key...

Bhavani Shankar.