That is one of the most sophisticated and well built homemades I have ever seen. I like the way you desgned the advancement system, though the tube the darts feed into looks like the edges got shredded (you did that on purpose right?). One thing, this is definitely not a sidearm, its more like a very compact primary, comsidering the clip's capacity. Good job and props.
It may be because the the rotating mech is jammed (in which case the is some sort of resistance in pumping the AT3K) or it could be the pump is not connected to the piece that causes the AT3K turret to rotate, in which you will need to connect them. Anyways, it isn't easy to help you if you don't post a picture of the problem. If you do, your question will be answered quicker.
Also, if you can't fire the AT3K, it may be because the round white piece on the firing pin that has a spring in back of it is not connected to the trigger (a certain part of the trigger fits in between the white piece's 2 small round sections), if that part of the trigger is in front or behind this white piece, the AT3K won't fire correctly.