I suspect that if you have your foot on the brake (and the gas) it disables some of the traction aids, but I haven't tried it again to confirm. I was having a problem getting ATRAC to work starting on a steep off road hill if I got on the gas before letting off the brake.
I know it will reduce throttle to keep the engine speed low enough that it can control wheel spin with the brakes. If you floor it, it might shut off. But I've never hear anyone say that happens. I'm not sure- just speculating.
Maybe the center diff is stuck locked and the center diff light is burned out or not working? That doesn't seem very likely.
Maybe try rebooting it: disconnect the battery for a while (at least 30 min, I think) and see if that fixes things.