<<< I have read that what I need is transparent bridging, and also that XPs netconfig prog does this automatically, but one machine must have BOTH types of connection, wired & wireless. >>>
I have no idea what "transparent" bridging is, no idea what XP's "netconfig program" is and you certainly don't need to have one computer connected with both a wired and a wireless connection to the router.
The most common reason for networked computers not seeing one another is a firewall blocking access. Have you configured any firewall software to allow access? At least one folder should be set as "shared" in each PC.
Each PC should be able to 'ping' the other.
In the network Properties of Windows 98 (right click Network Neighborhood and select Properties), click the File & Printer Sharing button and ensure one or both boxes are ticked as appropriate. If the Primary Network Logon is set to "Client for Microsoft Networks", when you boot the PC you should be presented with a Network Login box. It is important that you don't close this via the [X} in the top right corner, or press Esc, as this will prevent you from accessing the network.
In one of the PCs, open My Network Places (Network Neighborhood) and try entering the path to the remote PC into the address bar at the top, either by name or by IP address: