I have it set to 0% in Afterburner, but looking at the fan it's still spinning? How can I get it so that the fan completely stops? I'm using a reference 6950
It is unlikely that you will be able to get the fan to stop on the reference AMD HD 6950. Even at idle, that card is using over 20 watts of power. The power supply circuits are always running. The GDDR5 chips run at full speed (AFAIR) even when the GPU is idle. Couple that power use with a closed design, and you need to move air all of the time.
Quiet cards usually have an open design. This lets each memory chip and power transistor/choke have a small amount of cooling based on case airflow. These open cards can sometimes turn their fans off at idle, often that can only be done with a card custom BIOS flash.
You can turn a reference AMD HD 6950 into an open design by buying an aftermarket cooler ($50-90). You could also sell the card and buy a non-reference open card.