That is a 5V PS2 so all bets were off to be honest. Sounds like the BCR was not charging up or working.
"It powers up, but when I throttle down to zero and throttle back up, it only restarts and re-powers up. No forward or reverse. "
Again, just trying to cover the easy stuff because a least the board boots and makes sounds, however, it dying whenever trying to move at first sounded power pickup related, now on the bench with alligator clips, you remove the track interface electrical pickup and it gave you more symptoms.