You need the AP to have a DHCP server enabled, or you will need to manually set the wireless client's ip address, gateway and dns.
Sorry but I have never tried to set thiu sort of AP up.
Normally a seperate AP will just relay DHCP, etc.
You will probably need to configure Internet connection sharing on the PC before this will work, as there is no routing etc set up.
Adding an ICS bridge will set up DHCP and routing for you.