Unless you ran it without oil in the gas or without the air cleaner I'd not worry about the compression. If you can't get it running to your satisfaction with the OEM carb then what you might want to do, if you use this thing very much, is find a retrofit carburetor for it. Something like this, you will have to cross reference things and make sure it will work with your engine. Engine size, bolt patterns, throttle linkage, fuel lines etc. Notice these have low and high speed adjustments. No primer bulb on these, you shouldn't need it or the side plate with the primer bulb from your carb might fit on one of these.
All in all you ought to be able to get your OEM carb working well enough, sometimes a bread tie, the wire in a bread tie is useful to try to clean the little holes in small engine carburetors or a single bristle cut off from a wire brush will work. Have fun.