Ok, the battery that I had was indeed a lemon, but it turns out that there is a problem in my gun too. Even with a new battery that the shop supplied (which was tested on site with a gun that is extremely similar), the gun did not fire.

Can anyone tell me what is the most common cause for a click but no firing?

Most common cause IS that the battery does not have enough power/charge.
If a fuse blew, it wouldn't even click (if you have a fuse)

If that isn't the case, then check your wires, gears, motor, piston, etc... If there is something wrong, you'll probably notice something strange immediately.

You're JG is shooting 430 fps, even an 8.4v nimh mini can power that. I don't see why it has to ONLY take 11.1v lipos... So it isn't a power issue.

Yep you'll have to open it up to see what's going on in there... If you don't think you can do it, bring it to a gun doc.