Why does the power button not work?

The power button is jammed or something, and I can't get it to turn on in anyway as it's dead and it doesn't recognize the charger. How do I fix this, becuase I have important things that haven't been backed up yet, and I can't back it up because it won't turn on or connect to itunes when plugged into my computer?

I have tried holding down just the home button to get it to show something on the screen and twice it worked, both times as it was plugged in and it had the battery at red but it said it was charging but it didn't charge?