First of all, I only tinker with small engines, I do not know much about them!
Not familiar with goped engines at all, does it use the small square style carb like in a weed eater / chainsaw?
If so I would fully disassemble it, inspect the metering / pump diaphragms, remove / clean the needle / pin, and force some carb cleaner through ALL the little passages. Cleaning just the screen may not be enough and the diaphragms may be in bad shape. Also make sure you reinstall the diaphragms correctly. (your carburetor may be completely different that what I'm use to, so disregard if it is).
My newish push lawn mower wouldn't start after sitting for a bit, was only used a few times as I decided to use some junker mowers I picked up free. When I went to use that it wouldn't start for nothing, only a little starting fluid would fire it for a couple seconds. Turns out something plugged the jet in the carb, cleaned it out and it was good after that; it doesn't take much to stop fuel flow. Maybe the gas was going bad.
Have you sprayed starting fluid / carb cleaner into the carb and see if it will fire for a few seconds at least?
Can buy rebuild kits cheap, but you need to clean the carb 100%, if any passages / jets plugged, the rebuilding will be a complete waste of time. You can even get some brand new carbs dirt cheap on ebay.
I'm no expert so do some research on that particular engine. Most of the small engines are not too difficult to work on and info is easy to find on them.
Depending how old it is, a compression test might not hurt. I don't trust people with 2 strokes, may not have always ran the proper oil. Me and friend in the mid 90's got his sisters old moped out of their shed (she moved on to a car and left the modep sit), and we had no idea about 2 stroke engines. We ran it on gas only until someone seen us filling it up and pointed out it needed oil mixed in, oops.
Didn't kill the engine and I still have it, tore it apart last year, cylinder looks pretty good but had stuck piston rings, though it has sat since the late 90's.
Not sure what kind of kill switch those use, but make sure it isn't damaged or any wiring.
I thought there was a goped forum you were on, would assume they would be the best source to ask for help