Don't start redoing what you've already done. First thing you need to do is fix that pull cord or remove it and use a cordless driver. Now, I haven't seen any mention of compression... you can borrow a tester from an auto parts store, without enough compression the engine will not run, fuel will just blow out around the valves. I think you need to look beyond the carb now, if you still think it's a lack of fuel the plug should tell you, if so, replace the fuel lines and the filter in the fuel tank.