I found the problem. The files were named with .bak. After I removed that extension they appear on the Payment Module List.

Now, I've set up a country called Office Use Only with a custom Zone like this thread recommends:

http://www.zen-cart.com/forum/showthread.php?t=116029

When I use the Office Dummy Customer with the above country/zone in its setup, the check/money order appears as a payment choice like it should, but COD is not a choice. In the Payment Module both are set up the same way.