Can't you try something in the command line like:
sudo passwd root
Then you can enter a root password and use the root account.
I find that it's generally easier (and probably slightly safer) to log in via telnet as my user account, and then su to root. At least it takes a little effort...
I've had a broadly similar problem. I find that the mouse pointer disappears when the machine is woken from power-save mode, or the display size is reset. I can tab between apps and enter text into dialog boxes, and the like, but the pointer itself remains AWOL. Restarting from the Terminal will...