I bought a new PC where there is no port to connect the telephone line. As such, I am unable to send fax from this new PC. What should I do?

You've got two cost effective options.
First you could go buy a fax modem. They usually don't cost too much, you can open the case and install it (as long as you have a free slot in the cmoputer), insert the CD that came with it if needed, and you'll be on your way.

Second, there are email-fax services you can subscribe to, where you would just scan the page and not have to dial out... just attach it to an email or scan it into the program provided by the company you get the service from. It goes out from your system over email, and they take care of turning it into a fax on the phone lines. This works for incoming faxes, too, so you don't have to waste paper on printing everything out that you don't need, and you'll have an electronic copy of everything that you can easily file.

It's probably easier to set up the first option, especially if you want o keep your current fax number or you don't do a lot of faxing, but the second is easier to manage once you get it going.

Wow, I haven't seen a PC sold without a built in modem for years. Was this a custom job? Every brand I've seen from retail has one.

But if you don't have one, you could do what Chirs suggested or get an external modem, there are some that will connect to a USB port.