There isn't nearly enough data here to make any sort of assessment.
-Have you tested your connection settings from the phone? Try something like Speed Test to see if it can establish a connection.
-Does Wi-Fi stay connected or does it drop in and out? Does the Wi-Fi icon change to being grayed out? Does it turn itself off under your settings?
-Have you tried changing the connection type on the router? WPA2 to WEP, etc...
-Have you verified that the network is broadcasting an Internet connection from another device?
-Can you see the phone on your network from a computer?
-Have you tried pinging an IP address from your phone?
More than likely it's a DNS or DHCP issue. But I don't want to recommend any troubleshooting methods until the problem has been isolated.
Sent from CAMACHO, my Verizon G2 (VS980) running PAC ROM 4.3.
The Aphotic Chaotic
LG G2 VS980 (Verizon) [JB 4.3] PAC-man ROM
Nexus 7 [JB 4.2.2] XenonHD