AC,
What about one of those electric cars for children? My kids had one, a red jeep. Had a motor on each wheel (so didn't need a diff), proper accelerator pedal and two speeds. Used two rechargeable 12v batteries. It got left out in the sun a bit, so the plastic body went a bit brittle, but all the running gear still worked fine.
You might pick one up cheap in the local paper. Kids grow out of them pretty quick, and they take up a lot of room.
MD.