Of course you can, you just have to set it up correctly
You mentioned that you were getting a Linksys WRT54G router, did you get it or are you using different one?!
If you think that you have messed with one too many setting for adapters, drivers etc, uninstall the device and start again.
If you have DHCP running on the router, anything that is connected to it, wired or wireless, will be given an ip address, subnet mask and gateway address. Once all of your computers have an ip address of the same 192.168.*.* (or what ever ip range you have set) make sure they are all running on the same workgroup name - press windows key + pause break to bring up the System Properties box, then click on hardware tab then click on the change button at the bottom right - might be a different button for XP home. The next box that appears give you the option to change your computer name, workgroup name and the option to join a domain if available - the last option deffinately is not available with XP home edition.
Once you've messed around in that, set your name and workgroup, you will be asked to restart your computer for the settings to take effect. Once your back in, click on the my network places if you have it on your menu or go to network connections then click on my network places icon on the left hand side. Next click on the Entire Network icon on the left, then dbl click on Microsoft Windows Network and you should then see the workgroup name you have created on the machines you are wishing to connect. Dbl clikc on your workgroup name and you should then see computers that are in your Workgroup.
If you have the windows firewall running, go to your network connections panel, right click on your adapter and then click on properties. In the new box, click on the Exceptions tab, then make sure that file and printer sharing is ticked. Go back to your Entire Network View window, workgroup etc as before and then see if you can dbl click one of the computers and see if you can see the deafult share.
Make sure you have wireless encryption setup, WPA preferably over WEP.
Hope that helps some.