Do you have proper compression? If so, read on.
With the fiber rubbing portion of the points aligned with the flywheel key, set the points so that a .020 gauge will go thru but a .022 will not. That'll get you quite close to factory specs. With the spark plugs removed, the spark should jump a 1/4" air gap (testers available at any automotive parts store).
As "racerone" states... carburetor and/or the fuel pump are suspect. Clean and rebuild the carburetor. Kits available here.
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(Carburetor Float Setting)
(J. Reeves)
With the carburetor body held upside down, the float being viewed from the side, adjust the float so that the free end of the float (the end opposite the hinge pin) is ever so slightly higher (just ever so slightly off level) than the other end. And when viewed from the end, make sure it is not cocked.
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(Carburetor Adjustment - Single S/S Adjustable Needle Valve)
(J. Reeves)
Initial setting is: Slow speed = seat gently, then open 1-1/2 turns.
Start engine and set the rpms to where it just stays running. In segments of 1/8 turns, start to turn the S/S needle valve in. Wait a few seconds for the engine to respond. As you turn the valve in, the rpms will increase. Lower the rpms again to where the engine will just stay running.
Eventually you'll hit the point where the engine wants to die out or it will spit back (sounds like a mild backfire). At that point, back out the valve 1/4 turn. Within that 1/4 turn, you'll find the smoothest slow speed setting.
When you have finished the above adjustment, you will have no reason to move them again unless the carburetor fouls/gums up from sitting, in which case you would be required to remove, clean, and rebuild the carburetor anyway.
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(Fuel Pump Diaphragm Test)
(Two Hose Type Only)
(J. Reeves)
Note: This pertains only to the regular Two Hose type fuel pumps.
Leave the hoses attached to the fuel pump. Remove only the two screws that attach the fuel pump to the powerhead. Re-insert those two screws and install a nut to each of them so that the fuel pump is securely clamped together. With the fuel line attached to the engine, pump the primer bulb while observing the pressure/vacuum operating hole on the back side of the fuel pump. Should any fuel leak out that hole, the diaphragm is faulty.
If the diaphragm is faulty, the fuel pump will require rebuilding or replacing. Note that repair kits are not available for all fuel pumps, in which case replacing the pump would be necessary.
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Let us know how you make out.