I have a John Deere push mower with an early 2000s Briggs Intek OHV engine that I am fixing for a friend. the mower has spark, 60 PSI compression, clean carb, but still can't get it to even pop when starter fluid is sprayed through the plug hole. After that, I took the valve cover off, and everything looks to be fine, other than about an ounce of oil in the cover. I also examined the flywheel key to make sure that the spark timing was correct, and the key was fine. The mower is in really good shape for its age, so I am confused as to why it won't start. What should be my next course of action in troubleshooting the issue? Could it be valve/fuel delivery related?

Do you have spark at the spark plug (grounded to the head)?
 
Did you check valve clearances?
 
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Yes, I have spark at the head. I tested with an in-line tester, and the bulb was flashing strong. I have not checked the valve clearances yet, but would that prevent the engine from firing even with the starter fluid straight in the cylinder?

I recently used my in-line spark tester on a Kohler, which showed spark.
Pulled off that cap (2 cylinder) and NO decline in performance.
 
Pulled the plug, COMPLETLY CARBONED UP electrode. Spark wasn't sparking in the cylinder
just going to ground inside the cylinder...
 
I've also had (rarely) a plug spark outside the cylinder but would NOT allow the engine in run-
Swap the plug, ran great....  
 
Pull the plug, check it outside the combustion chamber.
Even with that, I'd replace with a new OEM spark plug (if it doesn't start).
 
If compression is low, IE; burnt valve, slightly open valve, all the starting
fluid will NOT make it run.  Check for bent push rods (which would show 
in a very loose valve adjustment). 
 
Also, 60 PSI is quite low.  Put a little engine oil(couple teaspoons) down the 
spark plug hole and check compression again. If compression goes up, you have 
worn piston rings..  
 
.
 
.

I would try a new spark plug. Then trying normally starting it backup. If nothing then check spark plug, wet, bone dry, gas smell on it?

Thanks for all the help! I took the head off, and there appeared to be a new exhaust valve, which lead me to test the valve clearances. They were both a little wide at .010, but my feeler gauge only went down to .008 so I tightened a little past that. Still it wouldn’t start. However, the plug was wet and smelled like gas when I removed it. I will try to get a new plug soon and test it. Also, to respond to SRTsFZ6, I have run Briggs flatheads at 20-30 psi, but compression could be a bigger factor on OHVs. Also If it is a valve seating issue, wouldn’t the PSI be lower than 60 if it is so bad that it won’t start? Thanks again for all the advice and I hope to get this running soon.
-Lincoln