The backfire means it's getting a spark and air, right? Just not the right amount of something, fuel + air + ignition.

Here's a super-basic one for ya. Have you tried a few drops of fresh fuel directly into each carb? Hardly the same engie but my old Yamaha 426 wouldn't start unless the fuel in the carb was like 5 minutes old. Yours sounds like a bigger problem, though. On the plugs, check the gaps, too. While they're out, soak them in gas in a plastic container. Metal container can react with the plugs and gas.

Keep in mind my knowledge is this: turn key, engine runs. Engine doesn't run, I call for help.

OK, back to my paper-pushing job where I can't cause much damage.