What type of A/V mod (composite or RGB)?
Does the RF output still work?Do you have any pictures of the inside of the FC?
I have a feeling that whoever did the mod either used incorrect components, didn't know what they were doing
or the game uses some "special hardware" built into the cartridge. Depending on the type of mod, there are a few games known not to work correctly. If I knew the answers to the above questions, I might be able to help.
EDIT: I re-read your original post and got the answer to my second question and I realized the issue is on multiple games.