OK, let's go through your problem. The paint goes in the paint cup, drains by gravity down into a central cavity where it is stopped by the needle acting as a progressive valve. The needle point is tapered and it fits into a tapered hole in the two-piece end cap (the rear part is called the Nozzle Cap and the very front part is called the Head Cap) so that when the needle pulls back the paint should flow through the hole. That is normal flow.
The needle isn't actually pulled back by the "Main Lever" which is the correct name for the trigger. What actually happens is the trigger pushes the Needle chucking guide back and it is that guide which clamps down on the needle by way of the Chuck clamp nut.
Now, the first thing you need to do is start at the start. Your Paint cup has a cap and right in them middle of the top there is a small pinhole that vents the cup. If no air can get into the cup no paint can get out, so the first thing you need to do is check the vent and make sure its not clogged. Just drop in L-thinner for a couple of minutes and then take as straight pin or a wood tooth pick and clean it.
Next place you could have a problem is inside the brush body; there may be an obstruction in there. Now you can soak the front half of the brush in L-thinner to clear such a clog but you have to be very very careful wen you do this to make sure you do not soak the part where the air comes in. Just submerge the brush to the cup, no deeper. The reason for that is that inside the air inlet passage there is a very small airvalve and it has a very tiny little O-ring on its top that will swell up and block air flow if it is soaked for more than a couple of hours. That's something you don't want to do.
The next two places to look are your Chucking Guide Nut. It needs to be firmly tightened by hand to grip the needle. If it is not properly tightened the chuck will move backwards when you pull the lever back, but the needle won't be pulled back and so no paint will flow - so that might be the problem.
The last thing that might be it - which is the first thing you should check - is the straightness of the needle. Just lay it on a pane of glass and roll it. A bent needle won't roll.
There - try those things and see if you can get it working.
On Edit :sillyme:: If forgot you had asked about the head cap. That front cap, the one that's properly called the "head cap" is just there to protect the very tip of the needle from contacting your work. You can unscrew it and get closer to your work, which results in a finer line, if you like. It has no functional duty associated with the actual spraying, it doesn't direct the air or paint flow in any way.
Kong