If the game runs, you can be pretty sure the PRG EPROM is OK.
With the UNROM cart, I'd guess either the CHR-RAM went bad or maybe the board is wired differently than expected? (I doubt it). Maybe you could put the original game on the EPROM to verify the latter. If you'd want, I could slap together a little CHR-RAM itegrity tester program.
For that NROM cart, I'd guess the CHR-ROM might have a wire or 2 in the wrong place. EPROM writers (the one I've seen anyways), have read/verify options. To check if EPROM is OK you could read it to a file and in DOS type "fc /b file1 file2" to compare the files.