Probably a difficulty starting the Mathematica Kernel (the part that performs the calculations).
1) Restart the computer and launch Mathematica from a terminal window with the -clean option,
mathematica -clean &
This will make sure all preference and other start-up files are reset to default contents.
2) If that does not fix it, does the Mathematica Kernel run by itself? The Kernel can be launched by entering "math" in a terminal window.
The bare Kernel has a plain-text interface, so you can just type 2+2
ENTER, for example, to verify that it works.
If there are error messages, send them to
support@wolfram.com with a description of the computer and OS level.
Copying and pasting the whole Kernel session into the email is usually convenient.