It’s a little problem I encountered while trying to run XAMPP. Clicking the checkboxes should be a breeze, but clicking the “Start” button of Apache does nothing, while MySQL seems to be doing just fine.
Question, are you running Skype? Chances are, it’s the one causing the problem.
Simply go to Skype Options > Advanced > Connection … and uncheck ‘use port 80…’. Apply, and you should be good.