I am going to assume you use windows XP. If you do This should be pretty easy.
2 questions:
1- does the hardware all work properly? this is a moot exercise if the ethernet card, wireless cared or router are broken.
2- what are your network settings?
to resolve the latter let's check out your control pannel:
START---> CONTROL PANEL
L---> NETWORK CONNECTIONS
L----> LAN (rigt click + properties)
In the window that opens, choose "TCP IP " from the list of availabilities.
click "properties once it is chosen".
Here are the options for aquiring your cmpt an IP address. be sure that windows is being told to collect a DNS address as well as IP address automatically. this should provide your Cmpt w/ the necesssary IP address.