Ed, thanks for posting your question. I hope that an actual modems-with-Puppy expert will be along shortly to help, but in the meantime I would suggest a couple things.
First, try using Puppy 2.11 (2.6 kernel) and also try Puppy 1.09CE (2.4 kernel) and tell us if one of them works.
Second, with Puppy booted, type "lspci" in a terminal and give us the output, especially anything that seems related to the modem. The more info you supply the easier it is to provide useful help.
Third, a lot of the Rockwell chips are softmodems and so they only function in Linux if there is a specific driver available. If Puppy doesn't have the driver, and you cn identify where to get the Linux driver, Barry will generally accede to requests to insert that driver in the next Puppy version.
BTW: the Linux kernel does not know what IRQs are set on your modem by Win ME (*shudder*). It should read what IRQs are set in the BIOS at boot time, though.