the major carb adjustments are Idle, fast idle, choke, and idle air mix.
None of them should prevent the engine from starting. When you hit the gas pedal, none of the adjustments do anything anymore, they only affect idle. The "adjustments" with the throttle open are effectively your metering jets. To get more or less fuel ratio at open throttle, you use larger or smaller jets to change the air/fuel ratio (usually to "adjust" for altitude). If it wasn't "jetted" for your altitude, the mix may be off far enough to prevent it from starting.
When you rebuilt it, did you replace the needle valve? Small brass fitting deal that goes in the bottom of the bowl. It cuts off incoming fuel when the bowl gets filled to the proper level. It's (arguably) the most common thing to screw up in a carb. If the float is set too low, installed wrong, or if you reused the needle valve (they get old and stick), it may be keeping the fuel from filling the bowl internally, so you may have fuel flowing at the incoming line and not getting into the bowl. If you take it off, flip it, and a fair amount of fuel comes out, you're probably OK.
Occasionally, you have the other problem, where fuel doesn't stop getting pumped in, the bowl fills completely, and the fuel can't atomize, but that is almost always a very obvious problem (liquid gas flowing down the carb throat and/or on the outside of the carb).
Does your choke open and close? should be closed with it being winter. That shouldn't keep it from running if you're using ether, but if it isn't closing, that certainly won't help...
there's a lot of little things that could also have been overlooked during the rebuild as well, and there are a bajillion differnt types of carbs, all with their own metering, valve, venturi, etc. designs... Best bet is make friends with a carb guy that lives close to you