My money would be on the carb. Something didn't work right in your rebuild. Were you able to remove the mixture screws and spray carb cleaner thru those ports? Like I said in one of my rants, this gasohol is gumming up lots of good 2 cycle things. I rebuilt a ryobi weed eater Zama carb lately. Around the fuel level channel in the carb base there was a substance that looked like RTV sealer that I had to scrape off with a small screw driver as even carb cleaner didn't take it off.
You've got spark and I think that you are getting enough vacuum. Instead of starting fluid just take a syringe or eye dropper and spray a bit of fuel mix into the carb throat. I bet it will run for a bit. I doubt that you have hurt anything yet but actual fuel mix will eliminate that possiblilty.
I assume that you when you depress your fuel bulb that fuel is coming thru the lines. Also be sure you have the fuel lines reconnected properly. The bulb pulls fuel thru the carb back into the tank. Its very easy to get them mixed up.
My 31 cc Mcculuch has been ultra reliable. But then, I always run it out of fuel and mix up a new batch the next time. I don't even know what kind of carb is in there and hope to keep it that way.
If its never been a runner, whats the compression anything less than 115 you may be wasting your time and money! Intake ,compression, power, exhaust. Start with compression first on any engine, step one compression tester.