My first advice would be to change out the tranny fluid. This isn't going to hurt the cause especially if it is brown. Simple pan drop and filter change w/ new fluid is all that is needed. DO NOT FLUSH TRANSMISSION!!!!!!!!!! < < < READ!!!! Even if the transmission is not your problem, that would help prolong the life. My guess via reading your symptoms is the tranny is toast. I had the same issue. If you want to possibly get along for a little while longer... try Lucas Stop Slip. It works wonders. Here is a little bit of read to help you out, search around that site offers a lot of information. Dave is a smart man with the 4T65E No Forward Cold
But!!!!!........ Since you said the car jumps and such in reverse, it makes me wonder if it's not something else like scotty said. A bad abs hub does not necessarily have to set a light, but majority of the time it does. Best thing to do is take it to a shop with a higher end scanner tool. Once again list scotty said it should be able to bring up any stored codes. Stored codes does not mean they will set the light off, just like an internal memo. That will give us a better idea if you make a list of any codes. But get it scanned, do a filter/fluid swap throw some stop slip in there and pray to the 4T65E gods.
