Many Apps not opening

I've found on the threads that many people have had this problem, but I've tried all the answers and still, many of my apps, when touched appear to start opening then disappear back to the menu screen.   I've tried Restoring the phone, downloading a free app, trashing and reuploading apps that don't work.  Nothing seems to help.  At first it was just a few apps that would not open, they were the newer apps that I've downloaded in the past few months, but now its infecting some of my older apps, and Instagram won't open (god forbid) anymore.   I'm wondering if it could be some sort of syncing issure but I've tryed unsycing the phone to itunes, etc. No dice.  Anyone have a solution?

Thanks,

C