If you're sure the console works, the only likely culprit is failure of the ROM chip on the cartridge. These devices are 40+ years old, and silicon is not impervious to age-related degradation, which can be accelerated by environmental factors like heat and humidity.
Unfortunately, the chips on these cartridges are mask ROMs and not re-writable, which pretty much renders the whole thing useless. If you're handy with soldering you could reuse the cartridge base board and build a cartridge emulator, but if you know your console is in good shape, and continuity between the pins and ROM is good, than the ROM is probably bad.