Sometimes there are simple clues available. I bought one a few months ago that hadn't been run in years. The only problem aside from a timed-out spark plug (which made it hard to start, but not impossible) was a stuck vent in the fuel tank cap. There was an obvious clue: when I pulled the starter, bubbles passed back up the fuel line from carburetor to tank. I just had to unstick the cap vent, and install a new spark plug, and it was good to go.
Lack of tank venting usually results in start-and-stop problems (runs for 15 seconds then stops) rather than no start. A split in-tank fuel pickup hose, or a blocked pickup filter, on the other hand, means no start.
There is a reasonable chance the fuel pump pulse chamber of the carburetor is full of jelly. Also, if it does not have an in-tank pickup filter, the filter gauze in the pump chamber may be puttied up with dirt. However you should check the simple external things before we get to that, and we need to identify the carburetor type before we talk about the fuel pump. BTW, the jelly-in-the-pump problem is quite likely to cure itself: the jelly is soluble in fuel, so if you get it feeding even a little bit if fuel it will recover by itself.
The main thing is, since you have spark and compression, and you seem to have access to plenty of fuel system parts from junked machines of the same type, this should be fixable without very much drama.
