Yes, since they blew the diagnosis and performed unnecessary work, you should be refunded the money.
Getting it out of them will be another question entirely.
Look at any paperwork you got from them. Is there a policy for refunding? Did you sign anything OKing the work before it was done?
I would approach them - talk to a manager - not saying that you think you've been taken, just that you think you were charged for unnecessary work, and even perhaps work that wasn't performed; after all, you are relying on their expertise, and they kind of blew it.
Just between us, I think you're probably out the money. If they don't make it right, then go to Angie's List and the BBB.
I am
Dawg