Blumbly, you might start with this thread, which in turn shows you how to access the right pages in the overhaul manual, on-line:
https://www.outdoorking-forum.com.au/forum/ubbthreads.php?ubb=showflat&Number=22526

Your diagnostics to date indicate a carburetor fault, or a massive intake pipe leak. Check the O ring on the inside of the intake pipe, just to eliminate that as a possibility. I've never known one to give trouble, but it only takes a moment to check that it is in place and undamaged.

Your carburetor is a PulsaJet, which is the more complicated of the two Briggs used on those engines. You will have to clean the intake filter on the longer suction pipe - they accumulate grass and crud from the bottom of the fuel tank. I doubt that will be your problem though: an obstructed suction pipe usually causes high speed lean mixture, not failure to start. Is the automatic choke closing? The engine will not start if it is not set up correctly. While you are at it, check that the top of the tank and the bottom of the carburetor are both flat, as explained in the above thread.

The next potential problem is the flaps on the diaphragm which are part of the fuel pump. The flaps need to sit flat and seal against the underside of the carburetor, when the diaphragm is laid flat on it. One is the pump intake valve, the other the pump outlet valve, similar to a mechanical fuel pump in an old car. The pump diaphragm is also part of that big diaphragm which also acts as a gasket between tank and carburetor.

To check the parts and put the whole thing back together successfully, I suggest you use the on-line manual I referred to earlier. The automatic-choke PulsaJet is easily the most complex carburetor I've seen used on a lawnmower, though it isn't nearly as complex as a chainsaw/trimmer/blower carburetor. Following the manual closely is much easier than trying to trace all the functions and work it out on your own.