I learned a while back that with cares, one thing can lead to another.
I had a starter go bad, same nasty smell and all... from what i can figure, it sent out a surge or something and fried a bundle of wires... I replaced the wires, and still nothing... I got hacked and started replacing everything between the steering column and the starter (that was related of course) and finally gave up and took it into a shop.
They replaced the 25 cent neutral safety switch in the transmission. (it screws into the outside like a plug and ensures your car is in neutral, no neutral, no start.) turns out when the surge went out, it had just enough juice left when it got to that switch to end it's life.
That being said, I agree, Jump it first. Make sure your belts are tight... you may have enough slippage so as your not getting a good charge, and, when you finally think you have everything fixed, take it for a nice long drive to make sure your battery is good to go.