Need a little small engine assitance, if possible...

If you put the carb in a strong cleaner made for that purpose, and left it in there for the allotted time, then the carb may not be the issue.
At this point I would be going back to basics; a compression test and a suction test. Just like your auto engine, these little guys are air-pumps. They suck air in and they push air out. So remove the carb, put your thumb over the hole and pull the starter-rope. It should try to suck your thumb in. If it doesn't, pull the muffler off and try it again. If the suction is now harder, then clean the muffler out. If no difference, and the compression is well over 100psi, then the crankcase may have developed a leak. But if the compression is under 90 then the ring is not working, time for an inspection. It may just be stuck. Or the cylinder may be scored. With the muffler off you should be able to inspect the cylinder through the exhaust port.
Good luck.
I can do the suction test, but I don't have a compression tester. I'll see what I can do with this, but it'll probably be this weekend. Thanks for the suggestion.