2002 Saturn L300 Car won't start

Background: Bought car not running. Past owner says that car would die when put into reverse. After third time into reverse car would no longer start.... Present known info: I have codes po601 and u2105. All fuses have been checked with a test light and ign. On. Fuel pump will not run unless relay is removed and a jumper wire installed. Crank and cam sensors have been checked and are ok. Car will start if someone cranks engine while another sprays carb. Cleaner into intake tube. Code 1780 showed up after that short run period. Pass lock seems to be ok because you can shift into gears after ign. On and releasing brake lock. Purchased a used ECM but would not help no start situation....A donation is acceptable upon receipt of a viable answer. Last answer given was much to general and really didn't help. Thanks