Every time you have a junk piece of equipment, that you may or may not be able to fix. Carefully take it apart. Lawnmower engines are tough. Usually, someone will hit a big rock or root, and the mower never runs again. It's because there's a key up top that times the spark with the engine. That key shears off and costs $1 to replace. Don't fuck with carb screws unless you know what you are doing. Fresh gas and a new spark plug works 80% of the time. Some mowers have a low oil cutoff as well. Then you check for point type ignition, and check for spark.
Pumps can be trickier. That pressure washer pump would probably not be hard to fix either. You usually have pistons, diaphragms, or impellor type pumps. I imagine that yours would be piston type. The engine moves the piston creating pressure, while a valve closes to keep the pressure there(check valve, or regular spring loaded). The packing or seals on the piston could be shot, or the valves could be leaking. More than likely, it was run low on oil.
Take it apart, and figure out how it works. Stare at it, and think about what would need to happen to create pressure.
Pumps can be trickier. That pressure washer pump would probably not be hard to fix either. You usually have pistons, diaphragms, or impellor type pumps. I imagine that yours would be piston type. The engine moves the piston creating pressure, while a valve closes to keep the pressure there(check valve, or regular spring loaded). The packing or seals on the piston could be shot, or the valves could be leaking. More than likely, it was run low on oil.
Take it apart, and figure out how it works. Stare at it, and think about what would need to happen to create pressure.