LAN connection between Windows XP Professional and 2000 Professional

I have a problem connecting computers running Windows 2000 Professional and XP Professional.  I can't get them to see each other, even using the DOS "ping" command to their IP addresses on the LAN.

I had been using two computers running Windows 98 and 2000 Professional connected to the internet through ethernet cables to a router with no problems.  I replaced the older computer with an Inspiron 300 running XP Professional, and have been unable to get the two computers to see each other, although I have no problem seeing the Internet through the router.  I first used the SP network connection wizard, including creating a network setup file for my non-XP computer, but in trying to use the file, I received the message:  "The Network Setup Wizard is supported only on Windows 98, Windows 98 SE, Windows Millenium Edition, and Windows XP.  Instructions for configuring networks for other operating systems can be found in the help files for those systems."  I have spent many hours trying to configure the two computers, including checking the options noted in the the reponses to earlier postings.  I know it isn't the router because I've replaced it with a wireless router and am still having the same problem.  As noted earlier, the computers can't see each other using the "ping" command, just returning multiple timeouts (I determined their IP addresses on the network with the DOS ipconfig command).  I suspect there must be some security setting that is preventing the computers from seeing each other - should I create MAC addresses for the wireless adapters on the two computers?