Pardon the insultingly obvious questions, but they needs to be asked.
Are you using fresh batteries?
Is the belt loaded in the proper direction with the nerf logo facing up?
Is the belt door completely and firmly closed? Theirs a switch inside the belt door that will prevent it from activating without a belt properly loaded. Try removing the belt, and reaching in to depress the pressure plate on the belt door with your finger and see if that gets things spinning.
Vulcan's are notoriously finicky and prone to breakage. The more common problems are stripped gears from people ripping the belts out instead of opening the door first, but even with a stripped gear, it would still clunk it's way into attempting to rotate the belt. A completely dead vulcan could hint at a bound gear, or serious electrical problem. An unresponsive trigger? Ick. That sounds like something is either broken or in desperate need of lubrication. Start with the easy and obvious first. Best of luck.
Changed the batteries with new ones yesterday. Belt is in properly, and the top jam door is closed. I know for sure the gears in the belt mech aren't stripped because I can advance the belt in manual mode just fine. The trigger's only unresponsive sometimes, like if I hold it down while priming (force of habit from slamfire guns). Seems like I'm gonna have to pop this beast open and see what maker her tick. Will keep you guys posted.