So I have the exact same issue but I'm sure mine is a bit more severe and probably done for.
So here is the case, I hit black ice and slid into the guardrail completely destroying the driver's side front end. Most of all the damage is cosmetic, no damage to the engine or tranny other than some broken lines and a pulley on the front. So I towed it home and luckily I found a totaled e46 that I got for parts as it would turn out cheaper than to buy single parts separately. So since the oil cooler line was ripped away causing damage to the radiator too I didn't want to move it because alot of ATF and coolant probably ran out. Got that repaired first and the car would turn on and move forward and backwards but obviously couldn't take it out for a test drive.
One day after some cosmetic parts replacement I decided to move it to a new spot and suddenly it will no longer go into drive. I can shift into D without a problem but the car will just rev up and not move, only moves in reverse. The transmission fault code is illuminated on the dash and when I put it into steptronic mode it shows an S and will not change gears. I did a ton of search and found many reverse problem threads but nothing for Drive problems until this thread.
So I changed the oil and filter thinking maybe the filter was clogged. Disconnected the return line from the oil cooler to run out some of the old fluid in the lines and the pump seems to be pumping oil just fine. Still no drive, only reverse without a problem. Could it be the transmission computer as well? Any suggestions. I have an extra e46 with complete engine and tranny I can use just want to reach easy tasks first before doing a tranny overhaul. (The spare e46 is totaled so I'm better off fixing mine as it only had damage to the front corner). Any ideas, pointers, suggestions, comments would be great.