Do I have a case against this mechanic shop?

Sounds like your motor was already on it's way out. It's like rushing someone to the hospital, the doctor tries to save him but he dies because it was simply too late. You'll get a bill but you wouldn't sue the doctor for being there. Make sure you know the facts, talk to him and let him explain what you paid for. You'd look really stupid to a judge if the shop couldn't save your car because you didn't change the oil or some other form of neglect. But hey, I could be wrong and he may be a rip off that needs to be sued. Be smart! Good luck!