Problem:
On start up Mathematica warns you of a "serious error" and advises you to quit.
Solution:
Don't choose quit, instead dismiss the warning. The next screen will tell you the name of a file that has been corrupted. Quite possibly the file will be:
~/.Mathematica/FrontEnd/init.m
Whatever the file is called, locate it, rename it and then restart Mathematica
Cause:
You may have exceeded your disk quota at the time that Mathematica was writing to that file (resulting in a corrupted file).