A True Story.
A client's wireless Internet was not working. Turns out the Airport Extreme was dead (Airport Utility could not talk to it, even after a hard reset). I replaced the Airport with another one and was now able to see the wireless network, but we still could not get onto the Internet. The problem was the Ethernet cable connecting the DSL modem with the Airport. The plug at one end of the cable would not stay in the WAN port of the Airport since the retaining clip on the plug had snapped off.
Check your cables, and be sure to buy good quality cables.