There's a couple things that could be causing this. One might be interference from the wifi power managment. Unfortunately, power management defaults to either ON or OFF, and can't be changed. There's a hack for it at:
SilentKnight PPC software hacks
Alternately, there may be something at the router end. Is WEP enabled? Do they have MAC addressing on to limit number of and identity of devices?
Can't remember off hand if I'd turned WEP on or off on the router when I config'ed it, and the first thing I did in trying to set up the PPC with the router was assign the MAC address for the PPC to an IP on the router.
The problem is not communications between the router and the PPC. They see each other just fine. The problem appears to be configuring everything so that internet requests from the PPC go through the router, to the desktop machine with the dial-up connect, and out to the internet.
In fact, I'm starting to think it may be either a matter of the PPC not getting the right gateway IP to know that its supposed to send those requests to the desktop machine, or just plain inherent in the fact that the desktop is running ME, and I'm relying in part on ME's ICS software to actually work. (and yes, I know, this would be a lot easier with a broadband connection, but you have to convince my parents of that one)
But I will definitely try turning wireless power management off on the PPC next time I'm visiting and get a chance to try it.