Someone else will hopefully pipe in and correct me if I'm wrong, but it sounds like you could have a range sensor problem. Which on our cars is called (I think) the MLPS (manual lever position sensor). The reason I think this is because:
There is no code P0701 that I could find, however
A code P0707 (7 mistaken for 1?): Transmission Range Sensor circuit Low Input.
A code P1701 (forgot the 1 on front?): Reverse Engagement Error.
I believe that the MLPS also controls your backup lights...which might explain that code? No clue other than this except that maybe the tranny is having internal problems. Code P1710 is Transmission System Trouble. Check the codes again and list.
Keep in mind since I couldn't find the code you mentioned that I might just be full of [censored].
