Failed to resolve URLs through WLAN

Over the holidays I took my notebook into another wireless network. When I came back I could not connect to the network. This had two causes:
First: The router which I used for a DHCP server had only an IP pool size of 4. All IPs where resolved. The pool size is not changeable. The cause for this was that I use an open WLAN over which all the gigs that received a new iPhone for Christmas connected. Rebooting the router cleared the pool and I could at least connect through the wire.
Second: This is more puzzling and I have not yet figured out the cause, but I found a remedy. Before resolving the first point my notebook could connect through the access point but could only access local pages. This was of course because wlan0 did not receive a IP from the DHCP server but used an old one witch fortunately did not conflict. After resolving the first point the wlan0 interface did receive its own new IP but still accessing URLs outside did not work though pinging an IP did. This suggested that the URL could not be resolved through a DNS. This was verified by checking /etc/resov.conf where no entries for nameservers could be found. Adding the appropriate ones solved it.
A possible cause may lie therein that the access point and the router do not share the same netmask (router: 255.255.255.248 and AP: 255.255.0.0). This would suggest, that the AP can see the router but the router not the AP.