Sounds like it's starting, it makes a fast cranking sound, I turn the key off,

More details available in the 'owners manual' about the engine cranking/starting sequence. http://repairpal.com/repair-shops

Found nothing in manual to help. Dealer charged me $120 said they found nothing, even though it did it in the shop. I've pretty much given up on the dealer. They said that they could change out the starter for $400, but they wouldn't guarantee that it would fix it

It ain't the starter! .. Suspect fuel delevery system which includes all applicable sensors... I like to have fuel system testing equipment AND scanner hooked up ready to go while diagnosing these kind of problems... I wish I could tell you exactly what the problem is but that requires hands-on testing to determine.