Stalls when you shift it in gear

I don't know if they're connected or not but they all occurred at the same time so I tell you the whole story. It started with the car running hot I couldn't never figure out why then I had someone bleed the system and the running hot stopped only to return again a little while later. Then for some reason out of the blue my battery just kept draining flat never had done it before. It sounded like sometimes when you go out there to crank it like the starter was locking up but you would hook jumper cables to it and it would fire right up. I can leave the car running for a long time shut it off go out there in a couple hours crank it and crank right up go inside come back out 30 minutes later crank it and be drained then one day the car ran hot and I pulled it over into a parking lot to let it cool down. When I turn crank the car up I found it I could not accelerate with the gas pedal it wouldn't do anything. But it would accelerate on its own it would start out about 2 mph about a minute later it would speed up to about 30 mph level out, you could hit the brakes stop it take your foot off the brake it would do the same thing. And there was a huge amount of air shooting out the tailpipe for whatever reason it never had done that either. But I let it set for a while pulled some fuses put them back in crank it up the problem went away then one day I was driving down the road the car ran extremely hot and slowed down to a crawl it wouldn't pick up any speed at all the lights dim to almost nothing the dash lights went out completely and I drove it at about 5 mph to my girlfriend's house. We have cables on it try to put a charge that everything the lights never brighten back up and it's still with 2 miles an hour until we hit a slight incline it stalled out and shut off and wouldn't crack back. I found later on that there was better acid all under the hood the battery was shot. So I went I purchased a brand new battery and I brand new set of battery terminals I put them in and I replaced the starter relay because it was burnt out and the run crank fuse because it was burned up. Then the car would crank right up and it would auto just fine but if you take it out of park it shuts off instantly no spitting no sputtering it just shuts off. You can also put it into neutral and crank it as soon as you take it out of neutral it shuts off instantly those fitting no sputtering it just dies. I've been told that it could be one of several different sensors by different people I've been told the camshaft sensor I've been told the throttle position sensor the crankshaft sensor the ignition relay I have no way to get it anywhere where I can run the code. So do you have any ideas?