I would check that the linkage from the F-N-R lever on the side is actually moving the lever on the side of the hydro. If the side lever is loose, it will not move the internal valving to engage either gear. You'll need an assistant, {or boss..} to move the lever while observing that the shaft actually rotates.
After starting the engine, the pump should be making noise if the clutch/brake has been released, allowing the belt to tighten on the pulleys. If the belt does not tension, due to binding linkage or rust or ???, the pulley on the top of the hydro will not spin and drive the pump. One other possibility is the pulley is loose to the input shaft of the hydro.
You could remove the belt, and try to turn the pulley by hand to see if it freewheels, or actually is driving the pump. If it is trivial to turn, and has no resistance, start looking for a replacement.
tom
