Most likely the main jet passage is blocked, and you will need to remove the carb, and give it a good cleaning. Check the pony tank for rust. This is a common problem, and it also should be removed and cleaned thoroughly, and sealer installed is recommended. This will prevent future rust problems, which can be a source of never ending grief due to condensation in the tank. Keep the tank full in humid weather, and use gas without ethanol if available. Available at your local small craft airport.
From the things you mentioned, I would check the compression. Pretty common to have a valve sticking or held open by a chunk of carbon. If you have good spark and good spark plugs (not necessarily the same thing!) your engine should have run on the starting fluid or at least popped, so I would go after compression. Doesn't have to have much over 50 -60 psi to run fine. They aren't high compression engines because of the rope start design. Also check the oil in the sump is not diluted with gasoline. Had one that absolutely wouldn't run, just pop a little. The oil didn't look too bad, but smelled of gas, so I changed it and it cranked up first try after that. Ended up cleaning and Red Kote sealing the tank at that time to eliminate the rust before cleaning the lines and carburetor bowl as well as blowing through all the passages in the carburetor with compressed air.
That pony was always sort of weak, but would crank the diesel if you babied it along and ran a lot of choke. I figured it was just worn out, didn't have a lot of compression etc. Lived with it like that for several years and then it sat idle for several years until last fall, I needed the tractor and got it in the shop. Disassembled the carburetor and drilled out the lead plug which blocks the passage across the bottom of the bowl from main jet to high speed metering well. Ran a drill bit through that passage and cut out a lot of rust and varnish and cleaned it thoroughly before plugging it back off with a drop of solder I collected by melting some rosin core wire. The pony has a lot of power now, cranks very easily, idles smoothly (which is nice to let it warm up before you load it) and is night and day different using it regularly from what I was putting up with before.
Also change your spark plugs, even if they aren't bad, then you will have a spare set for when you need them on weekend, after hours etc.
Anyone had the magneto off since it ran last? Have heard of ponies that simply needed the wires swapped on the magneto, or could be completely out of time.