Going mad with PC fax issues...?

I tried a free trial of online faxing. None of them went through and I had to argue to get the "contract" cancelled. I bought a fax modem in PCI card format, only to discover it was obsolete (it uses old PCI technology) and my state of the art HP PC already has an "internal modem"... very nice, but they didn't equip it with a telephone socket, did they! It runs off a cable internet connection, and we pay already for a separate land line for our phone. Does that mean I am simply going to have to buy a standalone fax machine, wasting paper, money and time because people haven't sufficiently moved into this century to start using email? I know faxes are supposedly "secure" but the GSM technology was supposed to be too! Or do I literally have to connect my 21st century computer to two separate networks, just to be able to send a fax from it? Please help, I am feeling underwhelmed with the idiocy of the situation, and looking forward to blowing up a certain Future Shop assistant tomorrow!