I don't understand how you're using the Access Point as a repeater. Do you have a wireless card in one of the computers that's using the Access Point?
When you say you ping the Access Point, are you pinging your Default Gateway's address (probably 192.168.1.1)? When you do ping, do you get a reply?
How are you checking network status? Are you doing ipconfig /all at the command prompt?
I recently (as I have several times before) set up a LinkSys Router/Access Point combination where I am using the AP as a repeater on the second computer. When I ping the AP it says that my packets are good but nothing is showing up when I check the network status.
I am using WindowsXP on both Pentium 3 systems and have a DSL connection.
I have checked everything that I know to check but cannot seem to establish communication between the two.