Some of those BT units are no fun at all. Check to see if yours is supporting enough HDCP clients.

As avainnovations suggests, probably the easiest solution is to turn OFF the BT's wireless, remove all of the wired devices, connect the WAN port of your D-Link to a network port on the BT, then connect the wired devices to the D-Link. At this point the D-Link becomes your wireless access point and router. Limitations of the BT unit are swept under the carpet.