Just for kicks, you could try to tighten the arm down. Under the cap at the base of the arm is a nut. Position the wiper where you want it and see if snugging it does anything. If not, they killed it. Hollywood is right, that thing is darn near cheap! Part# DLB500074.
Reread post, sounds like somehow the gear inside is broked. Still pretty cheap. Keep your receipt and let them pay for it. Whatever you do, don't let them do it. They've washed a billion cars and messed up yours, so if they have that kind of experience, I wouldn't let them first time takiing your car apart.