Good to see that you have some solution to your problem.
I do not think it is a firmware issue on your wifi router - 2004 is not that old especially considering dhcp came into existence a lot earlier than that.
Now that you have given more details of your set up, it looks more likely that this is more a routing issue.
Are you routing between the two routers or bridging the two? If you have two networks then the dhcp broadcasts from your LAN will not reach the dhcp server on the other network and this may explain why it does not work. Easy to check this - plug the PC directly into the wifi router (you will not be able to access the Internet but that is beside the issue) and see whether you can get a ip address.
Anyway, the only way to determine the problem is to sniff the packets on the wire - you should be able to download and install wireshark now that you have an Internet connection.