Access Point - No Ether Connection

I wonder if anyone can tell me if it is possible to have one access point "unconnected" (no ethernet cable) talk to another "connected" access point (which is connected by ethernet cable to the router) and manage to go out on to the internet. In theory I would have thought it should work strictly through the wireless with no ethernet necessary on one of the access points.

My problem is that everytime I plug the unconnected access point in at the mains I suddenly can not get the internet. I can connect to the unconnected access point alright but I just can't get beyond to the internet. I have tried setting the unconnected access point both with the gateway as the router and/or as the connected access point but neither works.

I have the unconnected access point set as "AP with WDS" but I have also tried it in "Repeater" mode to no avail. Security on both access points is set to WPA-TSK and working. I can also see the unconnected access point on the connected one so I know they are talking to each other. The router is set up as the DHCP server and DHCP is disabled on both access points and both have static ip addresses.

Before I completely lose it, does anyone have any ideas? Thanks in advance!