Ohm your stator and pickup coils before you order anything. More then likely, that is the cause of your problem. Everything you have described is nearly spot on for when these bikes have a bad stator, right down to "it won't start on it's own or with starting fluid, but I pull start it and BANG! fires right up". An engine needs 3 things to run: compression, spark, and fuel (needs air too, so really 4 things). If it won't start with starting fluid, you either have extremely low compression, or you have an ignition issue. Since it will eventually start on it's own, I'd lean more towards an ignition issue. However, if you have access to a compression tester, test the comp just to cover the bases (remember hold throttle wide open when doing a comp test). If that proves good, then you know for certain it is an ignition issue, and you atleast have some idea as to the condition of your engine.
There is an downloadable manual here on the forum, download it to get testing specs and procedures, get ahold of a mulitmeter, and possibly a comp tester, and take from there.