It sounds like your ISP is delegating a prefix, then? Weird, that all sounds reasonable to me. What do you mean the router gives up entirely, though? Computers in the LAN don't get an IP address? Packets go out but nothing comes back?
Yup, computers on the LAN don't get any address. From what I understand, the modem would be supposed to delegate a prefix to the router so it can hand out addresses, but this part isn't happening.