Is it (1) a dialup modem or (2) a cable modem?
Does (1) a phone line plug into it or (2) does your cable TV wire plug into it?
Does (2) the wire from your modem to the computer look like a phone line with a bigger plug or (1) does it have a "D" plug with about 15 or so pins in it?
For 1 you most likely don't have a NIC (Network Interface Card) or at least it's not being used. The "D" plug is a serial port (Same shape and size as your monitor cable, except with few pins).
For 2 it's most likely a cable modem that goes to a NIC card in your computer. And in this case it's being used.