The Wi-Fi Access Point is D-Link DWL-2100AP. It is protected with a WPA2 TKIP key, and the DHCP feature is disabled.
The AP is connected to a TP-Link R860 router (which does the DHCP) along with some other computers, and some others are connected to the network through the AP.
This way, all the computers on the network get an IP address from the same router and can see each other.