Meanwhile, back at the ranch ...
... Now that the DI-604 has proved capable of communication I decided to tackle the LAN problem - still with only two computers.
I started off by re-running the Control Panel "Network Setup Wizard" on both machines and followed that with a reboot on both machines, allowing them to settle down (a.k.a. taking lunch out of the freezer).
Nada.
I used the IPCONFIG command to obtain the addresses of the Laptop and BigBeigeBox. These I noted on paper, and opened up the Zonelabs firewall to check its settings.
I changed the settings there to establish the new identities, and chose (Zonelabs) "Apply".
At this point excitement overtook me, and I lost my one-change-at-a-time coolness, choosing to explore "sharing" on the drive Properties dialog.
I checked OFF "Share" and "Allow" in order to check both back "ON" which enabled the 'Apply" button, which I clicked.
At this point I have made 3 changes:
(1) Network Setup Wizard and reboot on both computers
(2) Firewall IP addresses updated
(3) File sharing renewed.
As a result of one or both of (2) and (3) both computers can now see each other through the DI-604 router.
My way is clear now to add the IBM server to the internet and the LAN.
Thanks again to DaveA and StuartR for establishing my confidence.
Also Leif who totally ignored my lovely 5-barrel pun the other day. Thanks Leif (grin!)
all round ...