My guess is that the contacts are still not fully connected to the carts somehow.
Maybe try shifting the cart slightly outwards when inserted? Might be a long shot, but also try loosening/tightening the 2 case screws near the cart slot. I had a lynx that didn't power on until I loosened the 2 screws....not exactly sure why, but it has something to do with pressure on the cart, cart slot and contacts.
The original lynx systems are quite finicky.
Good luck.