I've never had a problem with any A1181 topcase working on another A1181. I've used the old ones and the newer (silver) ones in both Core Duos and Core 2 Duos. If you use an older topcase on a newer machine, sometimes Software Update will download and apply a firmware update for the "keyboard", but other than that there is no difference, and it should be fully usable even before the firmware update is applied.
If your Core Duo topcase is known good and doesn't work on the Core 2 Duo, and the Core 2 Duo topcase is not working on the Core 2 Duo, I'd suspect something is wrong with your Core 2 Duo. You might want to try the Core 2 Duo topcase on the Core Duo machine. If it works, that means the Core 2 Duo computer itself has a problem, and if it doesn't work, then I'm confused. :-) If you don't have another actual laptop to test with, you might try taking everything to an Apple store, and hopefully they will be able to assist.
Also, I'm making the assumption above that you probably have a bad topcase, but on second thought it might be more likely be the computer itself. Do you get a light on the AC plug when you attach it? Have you tried resetting the PMU? Have you tried reseating the RAM? Have you tried a different AC adapter?