Thotil, after you restored it "as a new iPhone", did you use your older iTunes backup to get your data back (contacts, videos, photos, etc)?
The only reason I am asking is because after I restored my iPhone (just using the simple 'Restore' button), the iPhone worked fine; but started messing up after I used the Itunes Backup to put my data back. Possible corruption of the settings in the Backup? (That's what it turned out to be for me).
So, my suggestion is, if you still have the patience, try and redo the restore as a new Iphone, and then build it up step by step without using the iTunes backup (but make sure you HAVE EVERYTHING BACKED UP some other way). Chances are that it will work fine when the iPhone is set to the factory settings; you should be able to tell straight after the IOS restore (by checking the reception bars). From there, I used the simple sync option (as opposed to the backup) in iTunes combined with my Apple ID account to get most of my data back (apps, contacts, photos, videos, calendars ...). Some of the other settings/data I put in manually afterwards, BUT at least I have a working phone now. If you do go this route, please check your sync options before you do the restore (e.g. I synced my photos with iPhoto so I only had to resync after the restore in order to get the data back).
Hope it makes sense and that this helps.