It sounds like you are getting to gdm. Can you select single user mode (command prompt only mode) on the boot menu? If so, try to log in from there. Once you get logged in to a command prompt, create a new user with the command sudo adduser NEWNAME (NEWNAME is whatever you want). This will create a new /home/user directory for that user. Then reboot and try to log in as that user. It will probably work, which means some setting in your old /home were corrupted. The easiest thing to do then is just to copy your old /home/user data to your new /home/user folder.
Ok it sounds like you may have deleted a system partition. What I would do is make a live cd or better still thumb drive you can keep with you, then boot into that and mount your file system. Back up your /home partition (if it's there, it sounds like it may not be) and reload.