The Gateway P3C is an old one - so I'm speaking from memory since I have not come into contact with one of these in years. As I remembered it, this system does not have a built-in modem, so when you say it has a modem card installed, I'm assuming that you're talking about a PCMCIA modem, which is probably missing a dongle (the dongle is the part that contains a phone jack connector on one end, with the other end having a flat connector that plugs into the opening on the pcmcia card) and hence, no phone jack :o
A pcmcia modem without a dongle - and lots and lots of people will lose their "dongles" over time - is functionally useless. Although there are many sources for replacement dongles (look on eBay), it is probably just as cheap to buy a new pcmcia modem to replace your dongleless one. If you're looking to network the machine, you might even look at a combo pcmcia 56k/ethernet card - they'll come with two dongles: one for the phone line, the other for your ethernet cable. There are also pcmcia 56k/ethernet cards that have built-in phone jacks and ethernet connectors, albeit they're buikier because of the built-in connectors...