You don't need a modem, you need a LAN (also called Ethernet) port. Or if you prefer, a Wireless card, which will enable it to connect wirelessly (statement of the obvious there!).
There very likely is a LAN port - If you look for a sofrt of chunky phone socket (not the BT type of socket - but the sort used internationally, but chunkier). Or look in the hardware details under network adapters.
Control Panel - System - Hardware tab - Device Manager - Network Adapters. If you're in doubt let us know what you find there.