Modem works - Woo Hoo!
My Linux box is now back online! If you don't know the history of this, you can read about it here.
After getting entirely too frustrated with not being able to use the Linux part of my computer for anything meaningful, I embarked on a short and not-very-exhaustive search for a new modem. I found an eBay auction for the exact model that came preinstalled when I bought the box and which worked flawlessly with Linux. A couple days and one good bid later, I was the owner of a new modem. It arrived yesterday but I didn't have time to install it until just now.
OK - Booting windows, the OS saw the new modem and (re)installed the drivers. Good. I changed the modem that DUN uses and tried dialing into my ISP. Bingo.
Half way there.
Now - I rebooted and chose Linux at the Grub screen. It detected new hardware, asked me if I wanted to remove the old modem, asked me if I wanted to configure the new one, and took off without a hitch. Of course, it did that much when I put in the WinModem.
I always found it quite humorous that Linux knew exactly what kind of modem that was, but couldn't do a blasted thing with it.
I found KPPP hidden deep in the menus and queried the modem. It responded obediently, and I am typing this online under Linux.
Now I just need to find a decent browser...