Okay---here's an idea. It's possible that what happened is that your alternator failed and as you were driving, you were only driving on your battery's reserve power; once that started to drain, your car's computers (including the one that helps shift the transmission) started freaking out from lack of voltage---thus the weird shifting, the stall, and the inability to turn the engine over.
First thing I'd do is get the battery charged up (Don't Just Jump Start It). Put a battery charger on it.
Then start the car and test drive it (you can drive around a while even if the alternator is no good, but don't use lights, radio, heater, etc.). If the car works okay, then have the alternator tested.
That's about all I can think of that links these two separate problems of slippage and no starts.