This may help...
Try adding entries to each of the pc's hosts file (c:\windows\system32\drivers\etc\hosts)
This will work but only up and till the machines refresh their IP's, host files don't auto update to reflect hostname to ip address, thats where DNS does the trick.
IPX is only needed when your on a Novell network, thats it novell ver. 3-4, vers~ above support and use TCP/IP last I recall.
On the laptop that is not seeing the others, do a "ipconfig /flushdns" and "nbtstat -R", or just restart the DNS client service in services mmc or in the command console do, "net stop Dnscache" then "net start Dnscache" these will the clear the local cache on the machine, which would require the lappy to lookup fresh records of hostnames be it local or on the net, it will then cache those.
Just clear the caches of all the machines. Xp attemtps name resolution via netbios 1st (old school) then dns, since you don't have a dns server it's netbios for local resolution, dns for everything else on the net.