A couple things come to mind. The poppet valves in the fuel pump could get stuck with fuel turning to mush for a couple years. Some fuel will turn to a granular 'puddling' and make the valves fail to function.
The pickup 'sock' in the tank could also get clogged with rust and deteriorated fuel.
Get a lawnmower fuel tank and connect it to the fuel line inlet on the carb. Raise it above carb level, and attach/support. Fill as desired with fresh fuel. Attempt to start. If the problem is lack of fuel, it should start and run fine.
Depending, you may be able to disassemble the fuel pump and clean things up. Some have 'swaged' metal that holds things together, and you cannot do anything but replace those. Older pumps had screws and replaceable diaphragms & valves. Guess what you'll likely find...
If you think the tank is gunked, you can remove the Torx bolts holding the bed, and raise the front of the bed for access to the pump. Disconnect the fuel filler neck where it is attached next to the gas cap. It will be ok flopping around as you raise the bed.
Support the bed with some 2X4's or some logs, etc, do NOT go under the bed until it is safely supported. I use large pliers(waterpump) to loosen the ring that hold the pump and sender. Squeeze the tangs together too loosen, reverse direction to re-install.
If the sock is jammed with crud, cleaning the tank my be the only answer, or you could pull the sock, and install filters and/or sediment bowls/etc in the fuel line. Easier to change a filter than keep raising the tank to clean.
tom
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