Yup, you have probably toasted a set of clutch packs, but it could just be a shift linkage or maybe even a stuck detent ball. Unless you are mechanically savy I doubt you could do it yourself, but its possible. You need some semi-specific tools so that you can pull the snap rings, seals and maybe one of the races. $600 is pretty cheap, but I would bet it's another $300 in parts at least. If it's the clutch packs you will eventually not be able to go forward or backwards. If you are somewhat mechanical you might want to just pull it yourself and have them rebuild it, that will save you some money. Most auto tranny shops can rebuild it for you too, its a very easy rebuild for them.
I did mine the first time and had to do it again because I screwed it up. I do know how to do it now though... Its almost like rebuilding a Chevy Powerglide transmission, just a little different.