When gas is left sitting that long it turns to varnish...yes, the same color, smell and hardness of varnish used on furniture and floors.
You need to disassemble the carburettor and soak the parts in lacquer thinner overnight. The needle valves need to be blown out with an air gun after the varnish has thinned out.
If you want the easy way out, just get a new carb. The rest of the engine should be okay.