Very strange indeed - can't think of any in game settings that could cause this. Are all other controls still working? When you press brakes do the brake lights come on, can you flash your lights, change gear etc etc? The only time I have seen something similar to this are
1. When the lead connecting the pedals to the wheel has been pulled out or damaged, this causes all other controls to still function (except pedals) and the car will coast to a standstill and may appear to have stalled.
2. When the deadzone on the brake pedal needs to be increased because the brake pedal is regitering a constant press - although this fault would not occour after 1 lap like yours.
3. When another piece of hardware, or the software running it, have interfered with the working of the wheel or pedal set, again unlikely because of the 1 lap delay before it happens, its usually there when you get in game and, for me was the result of too many similar input devices on a USB hub.
Hope some of this helps and it would be interesting if you posted to say what it was, if you find out.