it seems something is wrong with your X11 systems (graphics user interface/GUI), hence why you are given a command, prompt because it can't generate your graphical environment.
The only thing i could suggest is a reinstall of linux, to refresh and overwrite any changes made to your X11 files which caused this to happen. If you have a seperate partition for your /home, then your data will be safe.
Other wise you'll have to find some way of backing up, prehaps from the command line interface, by moving the data/files to another partition (or floppy if you don't have lot of files) using the mv command, and mounting the partition.
If you have windows installed then you can use partition magic to create a logical partition, for your backup.
I hope i was some help...? If anyone else has any better ideas then suggest them!