You said "I've tried restoring to factory settings but it still isn't working." If the restore was success, that it went through all steps without error make an appointment at the Genius Bar of an Apple store since it appears you have a hardware problem.
Apple Retail Store - Genius Bar
Otherwise
Try:
- iOS: Not responding or does not turn on
- Also try DFU mode after try recovery mode
How to put iPod touch / iPhone into DFU mode « Karthik's scribblings
- 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.
Apple Retail Store - Genius Bar