....I was unable to take the entire carb unit off the engine, I could not figure out how....
These OHV engine/clone engines have a carburetor that is held on by two nuts and two bolts. There's usually two nuts that retain the plastic air cleaner assembly which in turn holds the carburetor onto the engine or intake plenum. There's gaskets between each piece so it's fair to assume your carb was stuck. Paper or rubber gaskets are like glue, especially on old engines. Don't forget to remove the throttle and governor linkages too, if needed.
I could be wrong about all the above though. Vanguards might be a different beast altogether...
Anyway, in these modern times, it's always going to be the carburetor that suffers after long term storage or neglect. The main culprit is corn alcohol in the fuel {ethanol}. I avoid it now altogether--
nothing but 100% gasoline, 0% ethanol.