more likely one of the ICs. its unfortunate they are all COB and blobbed like that...
do you have a programming device you could try to pull the ROM off with, perhaps?
its good you know the cart at least used to work. the battery is most likely dead, in a traditional setup this would only affect the SRAM's ability to hold data during power off,
but.... since everything is covered in goo who knows what they've done.
just speculating, but changing the battery might have an effect on the cart other than just allowing for data retention. i don't see why they would have integrated other features of the cart to be reliant on this, but its possible (if they wanted to not use a vreg is all i can think of, but that'd be a whacky decision to make).
thats really going out on a limb.
its something that is probably needing to be addressed anyways (the battery)