Try a reset by pressing the home and sleep buttons until you see the Apple logo, ignoring the red slider. Takes about 5-15 secs of button holding and you won't lose any data or settings.
Remove all apps from Recently Used list...
- From any Home Screen, double tap the home button to bring up the Recents List
- Tap and hold any icon in this list until they wiggle
- Press the red to delete apps from this list.
- Press the home button twice when done.
If still a problem restore with your backup.
If still a problem restore as new, i.e. without your backup. See how it runs with nothing synced to it.
If still a problem, it's likely a hardware issue.