10.5 Briggs Not Starting

I too have a swisher trail mower that had the exact same problem. Started easy and ran great until one day it just would not start. After trying everything I could think of, I checked compression and mine had none! The valve seat on the intake valve had popped out and was holding the valve open.
To check this, remove the spark plug, place your thumb over the hole and slowly pull the start rope. It should have plenty of compression to blow past your thumb. Just be sure you don't get bitten by the spark plug wire when doing this.

Yeah Walt, I read that part too. But the original post also says

I'm thinking I might have an intake valve stuck open.

Click to expand...

The one on my Swisher would also seem to have resistance when pulling the start rope but not enough pressure to blow past my thumb when I put it over the plug hole.
So the question is does it have compression or not?
The seat on the intake valve on mine would lift enough to kill the compression when starting but if it ever hit, it would run. After a couple more hours of use, it finally got to where when I would shut it down, the seat would fall out and hold the valve completely open.

When I repaired mine, I found this article about peening the seat to hold it in place.

PER Notebook

After peening mine, I just had to lap the valve to get the right clearance and it was good to go.