This sounds really odd, but I can think of 3 possible things (thinking electric, but similar types of issues could happen to nitro as well...though should be really uncommon on either).
1) Radio interference (unlikely if using a 2.4ghz, quite likely if you're not).
2) The electronics don't like being under load very much (in which case, use your warranty). To test, flip the car upside down and hold the tires (or hold a brush against them both to give more normal resistance and clean the tires in the process). Give it a little bit of throttle, and if it sticks, let go of the tires and see if it goes back to normal.
3) There is something about being in sitting track position that does it. Try compressing the suspension a bit while not on the track, and see if that triggers it. If it does, it could be some connections getting bothered by the movement in the suspension, and you just want to re-do those connections.
I don't promise it is one of those, or that there isn't a lot of other things to try as well, but that's how I'd start to rule out and narrow down an actual cause of "track only" behavior.