1998 Audi A8 4.2 - Heated seat doesnít cool -car wonít start

I was wondering if anyone could help me figure out what happened with my A8. I just bought it two/three weeks ago, and on Friday was
driving home and had the heated seat turned on. About half way there, I turned it off, but it didnít cool, and stayed on the entire way home. I started to wonder if there was a problem, but had some issues at home to deal with and didnít give it too much thought.
The next day I went to start the car and it is completely dead. The keyless entry wonít even work. My guess is the battery is completely dead.
So if I jump start it today, will the heated seat likely go on right away?
Do I need a new battery at this point?
Does the heated seat draw off the battery even if the car is off?
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