3rd party apps won't launch

I have done everything recommended by the Apple Support Community: I have re-stored (existing backup and new), re-set, re-synced. I have downloaded new apps, deleted old ones and redownloaded; have tried to drag and drop apps from Library to Devices; have reset my Apple ID on computer and pad, and currently have only one ID and then restored as new. Apple apps work fine. But not one 3rd party app opens. A short black flash on the screen and nothing. All the supposedly active apps' icons show in the "active dock". What am I missing?