Is your linksys behaving as a dhcp server? Is it handing out ip addresses? Who is your ISP... did they provide you with a static ip address or dynamic? Do you know your DNS ip addresses to use?
Those are a few questions we'll need answers toin order to help you fully. Basically at this point, you need to get internal networking working.
On both your computers you need to verify that the hardware (the network adapter) is working properly. Go to device manager and see what it reports under networking. If the two network adapters are working, you should have link light on the routerand on the nic cards.
The next step is to go to Control Panel --> Network and set your TCP/IP addresses; either "obtain automatically" if your linksys is acting as a dhcp server, or set these ip addresses manually. 192.168.1.2 with a subnet mask of 255.255.255.0 ; and the second computer with 192.168.1.3 with subnet of 255.255.255.0. Also make sure that you have file sharing enabled on bothcomputers ; and make sure that both computers have the exact same domain/workgroup (including capitilization). The 2000 computer does not sound as if it is properly setup.
Then you should be able to use Windows Explorer and setup sharing on drives/folders or printers, etc. on either or both computers. You should be able to see the two computers in network neighborhood as well.