I hesitate to even offer this, but from what I can see on the web, that model still has a battery which is user replaceable. If so - an I'm sure that you've tried this already as part of the card shuffle - try leaving the battery out for a couple of minutes and reinstall it, trying andytug's initial suggestion if it doesn't respond in the normal way. I'm presuming that the battery is charged - otherwise there wouldn't be anything at all to see.
A commercial data recovery outfit is perhaps the last resort but they will charge accordingly for even having a try. Good luck; we all can come to trust the integrity and reliability of these things too easily and get casual about backing up the stuff they hold. I've done it myself.