Well, since it won't boot or connect, your options are a bit more limited....
If you're comfortable, open up the phone (follow steps 1-6 of [guide|575|this guide]) and check out the power button area. Is there any obstruction with the power button?
The next step would be to [guide|580|replace] the [product|137004|headphone jack assembly] (which houses the power button).
Good luck!