chances are that the reason why it keeps getting the same IP address is because there aren't any other clients looking for IPs. so what's happening is the DHCP mechanism in your router assigns something like 192.168.1.10 to that computer, because .10 is the beginning of the DHCP range, and if no other clients need an IP number and that one's available, then, being the first one in the range, it will be assigned to that machine.

if you're really worried about the IP address, set a dynamic one. but, before you do that, try to ping an IP address from your machine. something like 216.239.35.100 (google). if you get a ping reply and can't access webpages via URLs, it's more than likely a DNS problem. check your DNS and gateway settings.