the WRT54GX4 has indeed 4 x 100 Mbit only ports (that's maybe the reason also FX Teleport didn't work too reliably)
i'm understanding both of your computers have only one gigabit port, so my recommendation would be to add a gigabit switch to the setup.
we had good results with a NETGEAR ProSafe GS108 8 Port Gigabit Desktop Switch but any similar model will do the job (don't go below EUR 50 / USD 70 to avoid purchasing some toy ...)
change your cabeling so both computers are connected to the switch and add another cable from the linksys to the switch (min. length per cable = 1 mt, better 1.5 mt for proper signalling) - nothing else needs to be changed.
however all of the above said related to connection testing would still be recommended or necessary (workgroup naming, enabling ICMP reply in the firewall on both computers, testing sharing, finding IP address of computers, testing basic connectivity using ping)
please note that WLAN routers often send a huge amount of so-called broadcast packets into your LAN (local network) so if not needed for something else try to disable the wireless function of your router (after connectivity tests from above are successful but result is still not satisfying)
please also note that if even without having the gigabit switch there is no connectivity between master and slave at all though pinging is successful there might be some firewall setting involved preventing communication and we would need digging deeper ...
hth, christian