When you were using WINFAX, your dial-up modem was ringing the phone line as a fax machine and not as a PC modem. It can do this because it sends PC data as essentially voice 'noise', like a fax.
A broadband modem doesn't work like that at all, so it can't pull the same fax trick.
There are some options:
If you have a free or very cheap dial-up ISP account, you could still connect up your old dial-up modem to the phone line and use it like you used to. As Ken said, add that filter on the end.
There is a VOIP fax format, but I wouldn't say it is widely adopted, or necessarily easy to set up. (And I have no idea if it works with your WINFAX software).
Or you can use an online fax service - you email the word document or whatever, and it faxes it to the number. There are even some free ones out there, but they don't always send them straight away (bad news if important, or sending to someone's house - it might call them at 2am).
Cheers!