Chosen Solution
Im having the same issue with a different mower poulon pr1842stc 18hp briggs. Exactly the problem your having and I dont know what to do. I even got a new solenoid and still having this issue with no crank unless i jump it.
@oneupondem , Mike, remove the spark plug and see if engine cranks over fast, if it does it is a compression release problem. Normally fixed by adjusting the valves to the correct setting. Use the link below to see how to adjust valves. Good luck. I hope this helped you out, if so let me know by pressing the helpful button. https://www.youtube.com/watch?v=PbYbSKN4…
