And it doesn't respond to a reboot...hold both the power and home buttons until the apple logo appears and it restarts, ignoring the red slider if it appears?
If none of that works, and it will not connect to iTunes in recovery mode, http://support.apple.com/kb/HT1212 then it is time for a visit to an Apple store genius bar to have the techs run some diagnostics.
If still problem try the remaining items of:
- Also try DFU mode after try recovery mode
- If not successful and you can't fully turn the iOS device fully off, let the battery fully drain. After charging for an least an hour try the above again.
- Try on another computer
- If still not successful that usually indicates a hardware problem and an appointment at the Genius Bar of an Apple store is in order.