I have exactly the same issue. All apps that have been downloaded from the store will not work. Ones that were part of the original build such as videos or Safari do.
The app pops up for a brief second and then disappears. It is very frustrating.
I've hard re-set. Closed down all apps. re-opened. Nothing works. I have dozens of the things and don't think re-installing them all is an option.
Any thoughts appreciated.