After taking care of some other tasks I got back on the problem. While progress is minimal at best, I do have some findings.
First of all, on the desktops with the WAPs, there are TWO IP addresses to worry about. One is the address set up in the WAP using the supplied CD. The other is the internal computer IP address set up through the system software. Of the two, the internal IP address is the most critical. You can actually communicate between computers with a WAP address for a completely different network, as long as the internal addresses are compatible.
So first I tried the 192 addresses. After setting WAP and internal addresses on each machine to be the same, the Win98 and the XP laptop would recognize a network of all three machines. The XP desktop refused to recognize anything other than itself. None of the computers would communicate, and the XP desktop would not access dial-up.
Then I set WAP and internal addresses to the Microsoft 169.254 configuration. Now the XP would access dial-up, and the two XP machines would show a three-computer network. The Win98 machine would recognize only itself, and again none of the machines would communicate. Error messages were varied depending on reboots, etc., but were along the lines of network connection could not be reached. Running the repair facility gave a message of Failed to query TCP/IP settings of the connection - can not proceed.
The laptop and only the laptop tries to set up an internal network bridge when I run the network setup utility. The bridge is unfailingly ineffective and even kills the ability of any of the computers to see any other machine. (The laptop is new as of January, the other XP machine is over a year old.)
I can get the laptop to communicate with either desktop by appropriate disabling of WAPs and reboots. I have been unable to get the desktops to communicate yet. Fortunately, having the laptop communicate with either desktop meets many of my requirements. If I could get the two desktops to communicate, that would take care of everything of real importance to me. (Distance-wise, the desktops are quite close while the laptop has been a couple of rooms away during these trials).
I have now gotten the Win98 machine to again access the internet, although it will not get e-mail. It keeps asking for the logon information over and over, never mind that it is the same as the internet logon information. I can even be on the internet, ask for e-mail, and get the repeated query. Fortunately something else I can live with.
Incidentally, I still need Win98. I have some legacy programs that will not run under XP, even in compatibility mode. No, they are not games, either.