Assuming it's a wireless router. Connect the computer to router by ethernet cable. Check the router setup screens (see literature which came with router or download manual for how). Once in setup check that wireless is enabled and that wireless mode is G or mixed mode (whichever matches your laptop). Disable Access List. Make sure that SSID is being broadcast. Temporarily disable wireless security.
Disconnect ethernet cable and check that you can now connect.
If so reconnect by cable and set up a wireless security type which matches that of the laptop's capabilities (if you can figure out how Apples terminology against industry standard terminology used in the router).
Apply new passphrase (or HEX code if your Apple still uses WEP) to Mac's networking section.