91 Camry auto tranny problems

I'm always getting dumped on by my friends, well this time it's a 91 Camry with a real wierd problem. When it is started up cold everything is OK. Even if it is allowed to warm up it is still OK. Then you shift into Drive and you may go 5 ft. or 1/2 mile and POOF, nothing. No forward, no reverse. You can sit there and play with it all you want, back and forth with the shifter and nothing. Shut it off, start it back up and still nothing except for maybe once in 30 starts. If you unhook the battery and wait a minute or so, hook it back up and start it, the tranny works fine. If you do a stall test it feels like it could break the motor mounts. Once again take off and you may get 1/2 mile at most and POOF. Mechanically the tranny is solid, and am really inclined to believe this an electrical problem. I can't seem to find in any of these auto parts store manuals any reference to the computers participation in the trannys operation. By the way this is a V-6 if that makes a difference. Much and many thanks in advance for any help anyone may be able to give as this one has me bewildered.