I'm going to try heating it up again tonight and jumping it from the car.
It's a bit strange though, I went to the store to look at replacement batteries, and it seems that my tractor has an ATV type battery instead of the typical Garden tractor ones. The main difference I can see is mine has circular posts rather than the posts with through holes.
Is there any way hooking it up to the car battery could do damage to the tractor/starter/battery? They both look like 12V systems to me..