LAN Connection Between Windows 2000 Professional and XP Professional

I have a similar problem as reported earlier regarding 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 had the same problem with the XP network wizard as reported earlier by "gdguide", and have spent many hours trying to configure the two computers, including checking the options noted in the the reponse to the earlier posting.  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).  What can I do?