You are right, my wireless router is a WRT54GS, I don't regularly look at the model number. In fact, the last time I looked at this router was about 6 months ago when I wanted to install DD-WRT on it, but because it is ver. 5, the flash was too small. But I digress, I would like the laptops to both be on the internal network so they can be used as web orbiters. I would try eliminating the router, but I don't have a switch or a hub to put into place of the router yet. I don't think that the router is the real problem, though.
I think that the problem is that I cannot get the Core/Hybrid to work as a DHCP server. Every time, I disconnect both the Vonage Router and the Linksys Router and set them up with DHCP disabled. Then reconnect them, then I go into the Network Settings under the Web Admin page and enter the data to run DHCP services at the core. When I connect either wired or wireless, I get an odd looking IP address with a subnet mask of 255.255.0.0 and I have no access to the internet and I cannot even ping eth0 or eth1 on the Core. I am at a loss right now.