Basically sounds me to like you need a way to make your computer pretend it behaves the way a conventional POTS phone does.
Traditionally, you interface with the phone line via a modem on the PC. Some modems allow for voice calls via PC, sometimes called a voice modem. If your'e cool with writing software or using a Hyperterm window, you can try controlling the modem in voice mode using AT commands and a software package. You can do pretty much anything to a phoneline by sending the right combination of AT commands to the modem. This assumes your'e cool with experimenting with the software.
For this use, I'd use a modem rather than implementing a hardware-based solution. One, because it is cheaper, and two, because your'e likely to get significantly better results with the debugged PC<->PhoneLine interface that the modem provides. You can make a hardware solution, too, but it may take a while, be expensive to figure out, and may not work reliably - but you'll learn a whole lot more. Depends on what you want to do.