Hi,
A little more info please, I will assume windows Vista. And your trying to connect using ethernet cable to a broadband router. The network status says connected but only local not local and Internet.
In network connections, right click on your local area connection (or wireless connection if your wireless) and choose properties. In properties double click TCP/IP, check that the IP address/mask/gateway/dns are all set to automatic. You may have it set for a reson so make a note of the number encase you need to put them back in when you return to your normal network. There are lots of other possible reasons but we'll work through the problem, if you check this for me and report back.
Compare the network settings on the working PC and the fault PC. (The IP addres is supposed to be different)
Regards,