When you say the G3 'shows a connection and a valid IP address', do you mean it has an IP address in the range handed out by your DHCP server (typically 192.168.x.x or 10.x.x.x)?
If it has an address like 169.254.x.x (which looks like a valid address), it didn't see a response from the DHCP server.
Assuming you are getting a valid IP, can you ping the G4, or the base station, or the router?
Determining what you can and can't ping will assist in working out where the problem lies.
If you can ping the G4, but not the router, then the chances are your default gateway is set incorrectly. check the TCP/IP control panel to see what settings you have.
If the pinging and default gateway look correct, then it may be the DNS server settings. Can you nslookup any address? If not, manually set the DNS Server address field in the TCP/IP control panel to whatever addresses the G4 has.
If it has an address like 169.254.x.x (which looks like a valid address), it didn't see a response from the DHCP server.
Assuming you are getting a valid IP, can you ping the G4, or the base station, or the router?
Determining what you can and can't ping will assist in working out where the problem lies.
If you can ping the G4, but not the router, then the chances are your default gateway is set incorrectly. check the TCP/IP control panel to see what settings you have.
If the pinging and default gateway look correct, then it may be the DNS server settings. Can you nslookup any address? If not, manually set the DNS Server address field in the TCP/IP control panel to whatever addresses the G4 has.