uhh.....i'm stumped

i have a 1996 saturn sl 1.9 liter DOHC....i replaced the coolant sensor then took it for a spin around the block and got it up to temp. to make sure all was working correctly. everything was fine, then i put it in park for a few minutes then went to put it in reverse and now it just all of the sudden started SLAMMING into gear. it's only happening in reverse. i talked to a few guys at work and they told me when certain cars' ecm's are receiving low voltage from the battery, it can cause malfunctions. i took a battery tester to test the battery and the battery was bad. i bought a new battery and put it in, then that solved the problem, or so i thought. i was recharging the a/c today and left the car running for a while when i finished. i got in the drivers seat and looked at the dash and the temp. gauge was all the way down, as if the car was off and the tach was on 0 as if the car was off, but the car was still running, but running rough. even the air bag light was flashing. I have a hunch that its the alternator but im no ase certified mechanic......please help:uhoh:

me thinks alternator, have it removed and bench tested

well if that happened with the a/c on, your belt tensioner could be bad. its a typical problem. so id check into the belt tensioner first, then alternator.