Actually, you didn't get screwed. Because if you did, you would have sent these scam artists their "processing fee" and you would be totally out that money. You never sent them a dime, so you are only out the $500 of your own money you already spent. Your bank can't make you repay the entire amount of the check, if you never got the money.
Always ask yourself - DID I EVEN ENTER A CONTEST? If not, you didn't win one.
Just because a bank or business exists (and found "online") does not mean it's legitimate. Anyone can create a company online just long enough to scam people. And anyone can create an "official" reference number. Here's one for this message:
20080517-COMPWIRE-1105PM-TEDCX