I've not seen that, but it sounds suspiciously like a low battery condition. But that condition normally results in a normal app related message screen telling you to put the phone on a charger.
Do you already have some backups made?
Like with Helium and Kies 3.0 ?
If you do, do a restore.
If not, I suggest that you try to make some, and then do a Factory Reset.
Your description sounds like something is really amiss with the OS. Maybe a file was corrupted or deleted?