Well, here's one key to the puzzle - you don't have a router at all!

The Linksys EZXS55W is a switch, not a router. See here.

So you have no router. You have no hardware firewall and the protection that comes with it. You have no NAT and no local private IP addresses. And you have an ISP handing out IP addresses to you that are not on the same subnet, based on the subnet mask that it is using. I'm unclear on how your windows systems talk to each other (you might want to post a traceroute between your xp and your win98 systems).