I have an update, and a good one at that! It wasn't the Cisco Aironet 340 series ISA card that enabled me to connect to my father's wireless network. Despite numerous attempts, even putting in the WEP key, it failed to connect.
I uninstalled the Sound Blaster PCI128 card, and removed it along with the Cisco, but not before uninstalling the firewall to prevent the 'blue screen of death' appearing and telling me about an invalid VxD.
With both cards removed, I inserted a Sound Blaster AWE64 ISA card in the PCI128's place, and put in a D-Link DWL-520 wireless card, the very card I originally got for the nearby Dell 2350. I was able to install the sound drivers without incident, and was able to get the external midi module to respond. Now the next thing. I was able to install the D-Link card, and after installing the Air Utility, I put in what was necessary to be able to connect to my father's network, and the computer connected to the network successfully at long last!
My only gripe now is that I'll have to get a CD-ROM audio splitter cable to go from both CD drives to the one CD audio jack on the AWE64. Until then, the E: drive will stay connected to the TAD input on the card so that the DVD-ROM drive can use the CD audio connector.