airport express wired LAN windows laptop

Cow Loon

I have a LAN with a linux machine acting as a router connecting to a DSL modem. I've connected an airport express basestation to a hub on the LAN and have been happily using my powerbook wirelessly. Now, mein girlfreund wants to connect her windows laptop wirelessly using a linksys wireless-g card, and 2 different weird things have happened.

First, if I configure TCP/IP manually, she can't ping the gateway. Using DHCP, she can ping the gateway and access the internet, but not the local LAN (pinging one of the machines on the wired LAN results in the host timing out).

My powerbook can connect wirelessly to other machines on the wired LAN. What do I need to do to get the windows laptop to work also?
Can someone explain conceptually what the issues are here. My linux machine is the gateway, with two NICs in it, one going out to the ISP, and one going to the hub on the LAN. Why could it be that the windows laptop can get out on the internet, but not access other machines on the LAN?