Wes, welcome to the HDTimeline forum. What you surmized with possible hole in the diaphram or carbon, combustion products hanging up the needle/CV slide assy OR the enricher/jets are partialy clogged with same. Hopefully if your tank is partially full, the weight of the tank will not be much (gas is 6.7 lbs/gallon), so if you remove the front holddown bolt and raise the tank GENTLY to not break the fittings or kink hoses, you should have enough clearance to pull the top cover off the CV carb, remove the parts (and the delicate rubber diaphram/slide will probably be pretty dirty) and inspect for pin holes or cracking, the needle retainer and the needle will have to be removed with a long tweezer. Since you have the aircleaner off and can lift the slide, you may want to use a old cotton T-shirt, wet it with Gumout Carb Spray (to prevent overspray from getting on paint or rubber parts) and wiping down interior a bit. Use a dentist mirror to inspect the throat area and try and clean out by wiping first...do not bend or use force on anything. Once you reassemble everything (notice how needle fits in retainer basket groove), carefully lower the whole works, including the spring, keeping diaphram center and bellows not twisted.
As Brian said, twist the throttle once and you should see a squirt of fuel if your carb is equipped with accellerator pump. If all is well, I would cover area with clean rags and spray 1 short blast of Gumout to "wash" the carb throat. Drain the float bowl (screw driver plug and capture gas drainings in a dixie cup...if you see a lot of junk, I would follow the rest of the posters AFTER you run the bike a bit, spraying short bursts of Gumout to flush the carburetor and if she runs well ONLY then consider rebuilding and cleaning the carb in earnest (this gives you a baseline that it was working before you do the carb rebuild). Of course you should have the exploded diagram of the carb in question , and since my post is long, go to the Self Help tab for details and diagrams...or the Search tab.
