firstly the real puppy site has a dialup forum if you still have probs
http://www.murga-linux.com/puppy/index.php?f=32
if you need to post there pls include more info on chipset or suspected chipset of windowsmodem or details of your new modem etc
2) Either click on Setup icon/connect to ...dialup....OR
open a terminal and type command (with root powers)
dialpup
which takes you to same gui config box....near the RH corner you will see a button called test and probe...redo it pls if no correct modem is detected at your com port
if you need to setup setserial first see this site
http://linux.die.net/man/8/setserial
In simple terms, if you have set or not set correctly the termianl (com port) your os can not talk to the external device