I am guessing that you normally use the Desktop shortcut.
See if you can start PAF from the Start menu (Start > Programs > FamilySearch > PAF5
If that works, delete the old Desktop shortcut, and create a new one by right-clicking PAF5 (in the procedure above) and selecting Send To > Desktop (create shortcut). Then shut down PAF and try re-starting it from the new shortcut.
If that hasn't worked, download PAF and install it again. You can download it from www.familysearch.org (on the right-hand side of the screen) If that solves the problem you should be on your way. If it does not solve the problem, you will need to uninstall PAF and install it again. If so, let me know and I can give you further instructions.
Once PAF is installed, you may need to ask it to search the hard disk for your PAF files, unless you know exactly where they are located.