All apps suddenly started to crash randomly - iPhone 4s, iOS 5.1.1

Hi,

I have an iPhone 4s with the latest iOS installed (5.1.1, no jailbreak). It always worked fine up until a couple of days ago, when suddenly all apps started to crash in a random time between 1 seconds and 1 minute after I open them. This applies to ALL apps, both native and third party apps.

The only thing that changed between the time it worked and now is that I installed SmartSync (syncing facebook and address book), I don't know if that is the reason for the strange bahaviour, but I deleted the app anyway. Still now working.

So, I tried restarting the iPhone, as somebody suggested on other threads. Nothing changed.

Next, I try resetting is (power+home button for 10 seconds). Nothing changed.

Next, I restored the iOS through iTunes. It reinstalled everything and restored the latest iCloud backup. Nothing changed.

Finally, somebody mentioned that installing a new free app would fix the problem, it seemed to work for a lot of poeple, but not for me.

It appears that my only remaining hope is to restore the iOS again, without using the iCloud backup (which might be corrupted, thus the source of the problem) and reinstall alla applications by hand. This is a hassle, and I'd like to avoid it (plus, I'm not even sure my paid apps would be downloaded without having to pay again. Would they?).

Any ideas?