sounds like the cards are just a tad worn or something. I have a few games that like to be in just so, or they won't load.
On one of the ones that worked, keep inserting it and turning on, and try shifting it about each time (not with the power on, dunno if that might kill the game) until you find the sweet spot.
My Arcade Duo card doesn't like being too far in, and my Cyber Core likes being to the right.