I remember working for a Saturn dealer back when that car was new. The number one source of all those problems is the alternator. Have it tested. It can cause the hard shifting. Sounds like the alternator died and you were running on the battery alone until it just became too discharged.
I recently started having trouble with my car in which it would shift gears hard, and was sluggish when it first started. i also found i had a leak with the transmission fluid so i believed it was just low on fluid but i kept up with fluid, and it still shifted hard so i was going to have it fixed. unfortunately before i could have this fixed my car died on my way, at first the gas just stopped working, and would not accelerate, after turning into a parking lot the car died completly losing control over the brakes and steering because they were power. the car will start but immediately will die. if any one has any idea what it could be i would be very thankful. i have heard from some people that it might be spark plugs, sensors, i personally think it might be trasmission, the fact it starts but then dies prolly indicates an electrical problem though.