Geez ~ it is very difficult to diagnose an engine problem when you're half way across the country. I will certainly agree the former comment that the level of fuel in the tank has nothing to do with your problem. As long as the carb is receiving fuel, the level in the gas tank is insignificant. The fuel to air ratio is determined within the carburetor, not the fuel tank.
The misunderstanding of the choke position is a very legitimate point. When the choke is "off" (not deployed) the cable linkage should have little to no tension. When the choke is "on" (applied), the choke cable should be tight and pulling the brass choke plunger up into the upper chamber. Try moving the choke lever (on the handlebar, or wherever you mounted it) and at the same time using your other hand to feel the movement of the cable on the top of the carb. When the cable tightens, you should be able to feel the increase in tension. When the choke is off, the cable should be relaxed.
Another point - which may not be the way "everyone" does it - but it works for me. First, tighten each external carb adjustment screw down - and COUNT THE TURNS - and write them down on a piece of paper if necessary. That way, you will know what your current settings are, in the event you want to go back to that setting.
After both screws are turned to the right and closed ... open each adjustment screw 1/2 turn. That should be enough to allow the engine to start. Crank the engine, ride it a minute or two, to ALLOW THE ENGINE TO WARM UP! Then stop your bike and leave your engine running.
If it is idling too fast, slightly open the screw on the right a little bit at a time. Maybe 1/8 turn or so, and carefully listen to the tone of the engine. The right screw (while looking at the carb) serves as the idle adjustment. Opening that screw allows a little more air to be introduced to the ratio. At some point, you should be able to achieve a proper idle.
Be sure that the choke is NOT deployed - and try riding the bike again. If the fuel is "too lean" or maybe "too rich", and does not properly respond to the throttle, then stop and tweak the "left" adjustment screw a little. There is no good way to explain the difference between too lean and too rich, but I will give it a shot. If it is too lean, it will be like the engine just quit running. You will have no response, because it is mostly sucking air. If the carb is too rich, you will commonly hear the motor make a "EWWWWW" noise. It is getting fuel, but not enough air.
You should be able to find a "sweet spot", where the engine idles and responds to the throttle. If continued tweaking of the left screw does not give you good results, you will need to move onto something else. This method will help to determine if the problem is an external adjustment issue.
You might get lucky and find that the real problem was simply an incorrect adjustment. After some trial and error on that and you still have to use the choke to get the throttle to respond, I will say that you are not getting enough fuel into the combustion chamber. (too lean)
One way to increase the fuel is to move the clip setting on the carb plunger to a richer setting. I think the "default setting" is in the second notch, which may be too lean for you. Move the clip to the #3 position. That might then fix your problem.
I do understand that some of the things that I have tried to explain may sound like a lot of Greek to you, so I found a web page that has photos and descriptions of the CNS carb. It may not look exactly like yours, but it should be pretty close.
http://kcsbikes.com/topic.asp?TOPIC_ID=121
The link may not appear as HTML, so you may have to copy and paste it into your browser bar.
Anyway ... if one of us other guys was nearby, we could probably having you running in a few minutes. But, that ain't the case, so you'll probably just have to attend the University of Hard Knocks, until you get it figured out. Every day is a learning experience. At some point, it will begin to "click".
Good luck,
Old Skool
