John Deere tractor help???

I have a 1971 john Deere 2020 tractor (I use it almost everyday to feed horses), a week ago it died while I was using it. I tried to start it again, the engine turned, but didn't start, so after about 5 seconds I turned the key back to the off position. But the engine kept turning, I had no control over the engine except to let it die on its own. I tried to pull the cables off the battery, but they were too tight. The cables burnt up, into flames, I put snow on it and got the flames out. So we pulled it up to the barn with the truck. I replaced the cables. We believed the problem to be the solenoid, so we replaced that. Once we replaced the solenoid (yesterday), it worked fine. But tonight it did the same thing again, but it died before the cables burnt up. I can't find anything on Google, so here I am, hoping that someone here may be able to guide me in the right direction.. My only thoughts are maybe the key switch?? Any help is appreciated (it's a pain to pull out round bales with the truck)!!!

John Deere tractor help???