Does the ME PC have "File & Printer Sharing for Microsoft Networks" installed?
Is its firewall software configured to allow the other computers to access it?
Assuming ME's Network Properties are the same as 98SE's, have you clicked the "File & Printer Sharing" button and ticked one or both boxes, as appropriate?
In the Bindings tab of the TCP/IP Properties for your network adapter that connects to the router, are both "Client for Microsoft Networks" and "File & Printer Sharing for Microsoft Networks" both ticked?
You could try using an alternative protocol, such as IPX/SPX or NetBEUI, for your file sharing, although it would have to be installed throughout the network.