Your broadband connection is not capable of faxing because it doesn’t have the ability to call anyone. You’d need a fax capable modem, as you know, to do that.
However, there are services that kind of “update” the idea of faxing. Services like jConnect (j2.com) will allow you to scan and send faxes through your computer, and with a provided number, you can receive faxes in your e-mail inbox. It’s not free, you’d be looking at around $15/mo + 20cents per page, but if you really need fax access, you can do it without the hardware and headaches.