Your ISP doesn't matter at all. However, how your base station and AirPort card are set up DOES matter.
You say your computer finds the base station. Are you using automatic addresses (also known as DHCP)? If you manually assigned your computer's address, that's probably the problem; you also need to tell it a DNS server and Gateway address. If you "obtain an IP address automatically," your computer should get all that stuff along with its DHCP address.