On a technical level, the DSL modem doesn't know what's communicating with it. My past routers (Linksys wireless, Linksys 4-port wired, D-Link 4-port wire/wireless, Inexq 4-port wired) all have complied quite readily with the modem. On occasion, I plug the m0n0wall box back in with a glimmer of hope, but I guess hope alone is not enough.
My ISP sent me a new DSL modem to try to work the problem out. I'll redo some tests with the new hardware and see what happens, although I honestly don't expect much.
It's too bad because while it was working, my m0n0 box was arguably the best router I ever had.