The valves won’t help the engine turn over.
Actually they will.
When you try to start it with out jumping it, does the engine turn at all? or just very slowly, or quick then slow, quick then slow.
Just to rule out mower wiring issues, disconnect the mower battery, now get your jumper cables, hook them up to your mower battery, and the other end NEG - hook to a good ground such as a engine mount bolt/non painted surface, then touch your red lead end to the starter + lug.. Don't be alarmed there will be some sparks, but if it cranks normally doing it this way, you have a mower wiring issue. if not, probably a battery issue or engine issue.