Chrysler Repair: Battery light comes on, transmission stalls, driving wheels, chrysler dealer

Question
I noticed about the car is that when drivin, the battery light will come on and the transmission stalls in Drive and Overdrive.  It's electronically shifted so I figured changing the alternator and battery would have fixed that problem because the volts were low when I ran a volt test on it.  A Chrysler Dealer here suggested changing the Alternator Plug.  Other than what that the dealer said i don't know. Like I said, I've only had the car for a couple weeks so other what I fixed I don't know much more about the car.  I just want get this car out of my drive way.  No reserve after the starting price. this is a car I am looking to buy and I know i might have to put some money in it any help would be great thanks in advance

Answer
Hi Steve,
To be of help, I need to understand better what is going on. So tell me exactly what happens. So far you tell me that while you are driving the battery light comes on. And the transmission stalls in either selector setting. By that do you mean that this happens, light coming on and the transmission stalling, occurs simultaneously? And when you say the transmission stalls, do you mean the car looses power like the engine is stalling or do you mean that the engine isn't affected but the transmission won't apply the engine power to the driving wheels? And do you cost to a stop with the engine dead or does it continue to run but the transmission won't drive the wheel until when? And if the engine dies does it start right away? I'm try to figure out how far 'dead' the electrical system is: to the whole car,to the engine, or just the transmission?
Did you replace the alternator and the battery? What is the history of the car as far as you know it?
If you let the car idle and try flexing every electrical cable that you can find under the hood does any one of them cause a response or failure of the engine or the light to come on (this may take two people, one to watch the gauge)?
I'm thinking the far ends of the battery cables need to checked for loose connections. Particularly look at the ground wires attached to the - post clamp where they bolt into the frame and where another branch of it bolts to the engine.
When you 'inherit' a car like this it is challenging.
Write me back with clarifications and results, please.
Roland