IOS7 appears to have been installed on my Iphone 4. It comes on, apps start but then the "restart screen" appears after 1-30 secs. After another 20-60 secs, the "restart screen" disappears and the app begins where it had left off.
Just to be clear, by "restart screen" I mean a black background with centered white apple and a progress bar beneath the apple. The progress bar lights up to maybe 1-3% but never any further (and sometimes less) no matter how long it remains in this state.
Best Answer
If you have a recent backup (and thus aren't afraid of doing a fresh install and restore), there are a few things to try - all of them involve putting the phone in a mode that makes iTunes prompt you to do a complete restore/update/sync afresh.
If that doesn't help: