Thanks, Tom and Mike for some fine advice, and thanks for the sympathy, Ellen!
When this computer was first installed, it seemed to work fine. Over time it has had more and more trouble keeping connectivity. At first it was just the internet and over time has shifted to not even being able to find the wireless network.
We've done all the work with the WEP number, have plugged and unplugged the router, have tried a few DOS commands recommended by UncleVic, but no joy.
Finally, after much googling and searching online (not on THAT computer, I dare say), we have determined that the adapter is not compatible with Vista. It is an external adapter and was simply moved from the old XP computer to the new Vista one by a family member who shall remain nameless but fancies himself a real 'puter geek. Ha.
We even paid for some firmware which guaranteed it would help. But it looks like the new adapter is the way to go, and supposedly (fingers crossed), it should remain an invisible change to both other computers and the router. But I do suspect it is more than time to update the router. But one thing at a time. Who's got all this discretionary income? Not us.
So thanks. I'll let you know if we are successful in this step.