When I click on the Mozilla icon, nothing happens. It does not open.
Every time Firefox opened
Mozilla/4.0 (compatible; MSIE 8.0; Windows NT 5.1; Trident/4.0; .NET CLR 1.1.4322; InfoPath.1; yie8)
One of your add-ons might be the culprit. Try running Firefox in Troubleshoot Firefox issues using Safe Mode. If that solves the problem, see Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems and possibly Troubleshoot issues with plugins like Flash or Java to fix common Firefox problems
If that does not solve the problem, create a new profile Then, Recover your data from the old profile. See http://support.mozilla.com/en-US/kb/Recovering+important+data+from+an+old+profile