Re: problems
A couple of other things to check before you spend serious money on anything:
Make sure the fuel filter and bowl are clean and without ANY water. If you have a "ceramic" type fuel filter, you can run it through your microwave to insure that it is not being obstructed by water. Otherwise just buy a new one, they're cheap.
Drain and replace any old fuel with new, fresh fuel.
Gently, ever so gently, tap the carb float bowl to insure that the float is free to move and allow fresh fuel into the engine.
Check fuel supply by going to full choke, going to WOT, priming the pump and crankning vigourously. Just put your nose in the area and take a good sniff and look, you'll know if you're getting fuel into the intake. If not, then you know what is your problem.
If it was running well when put up for storage, the ignition is most unlikely to be the source of your problem. Ignitions don't change from being stored. Fuel systems do, they build up varnish, clog, get sticky and develop strange ailments.
Note, running the engine "dry" on shut-down DOES NOT remove all the fuel from the intake systems, carb and such. That can only be done by disconnecting and using compressed air to blow out all the passages. In the future, use something like "Sea Foam" to shut down your engine.
Good luck, your fix should be really inexpensive.
Gary