Hi Aaron, welcome to Outdoorking.
When you run out of fuel, the engine sucks up whatever garbage is lying on the bottom of the fuel tank, and this often blocks up one of the filters in the carburetor. I think you will need to remove the fuel tank and carburetor from the engine, then remove the carburetor from the fuel tank. At that point you will be able to see both of the fuel filters. One is on the end of the long white plastic tube that reaches down to the bottom of the fuel tank. The other is a sort of a tubular mesh cover over the short, thick pickup tube. Please inspect both filters, and clean them with carburetor cleaner. Also clean out the shallow well in the top of the fuel tank, which the short pickup tube sucks fuel from. You should then inspect the main jet in the bottom of the short tube, and squirt some carburetor cleaner through it. Be very careful reassembling the carburetor to the fuel tank: the thin rubber diaphragm in between the two is fragile, and must be reinstalled exactly as it was to start with, on the same side of the gasket.
Please ask any necessary questions to have a clear understanding of what you are doing.
