Outdoor Power Equipment and Small Engines - Probable loss of compression on 4hp B&S Quattro

I have a Murray mower powered by a 4.0hp Briggs and Stratton Quattro engine. It stopped working at the end of the 2005 season, and it hasn't worked since. I have replaced the spark plug, replaced the gasket and cleaned out the cylinder, and it still will not run. It does not appear to have any compression in the stroke, which lead me to replace the gasket. I also cleaned out the cylinder, and, while I had the head off, checked the movement of the valves. They work fine for most of the cycle, but on the compression stroke, the exhaust valve lifts slightly. I think that the lifting of the intake valve is preventing pressure from building up in the cylinder, and preventing combustion. When I try to start it the fuel will ignite occasionally, as I can hear it pop sometimes. What has puzzled me is that I thought that the timing on these engines was fixed, so is it possible that either the valve needs to be re-tensioned, or the timing system has become damaged?

Edit: I found out about the starting compression release that is present on many B&S engines, but I did do a test by spinning the flywheel in reverse. There is no compression, and I have compared it to my other mower, and there is a big difference in the feel when slowly pulling on the recoil starter.

The model # is 10A902, type 2286

Any thoughts, suggestions or help is much appreciated.

Is there a possiably that you might've hit something back in 2005 which cased your mower to stop running?
Judging by the (((pop))) you say that your engine has, sounds to me that you've got a sheared flywheel key.This little piece of Aluminum is what keeps the ignition system in time.

Take the shourd (recoil cover) off. The flywheel nut and flywheel.The flywheel key is the short pice of Aluminum that fits into the keyway cut into the flywheel and the crankshaft.


BUT


Tip the mower over,muffler up.slowly pull the pull rope and watch the blade and crankshaft.Does anything wobble?(Watch the blade nut,does it wobble)?
If so your crankshaft is bent and further repairs might not be worth doing.
Since a bent crankshaft,while running makes a mower Vibrate.

Something else to consider is the valve clearances.

"Judging by the (((pop))) you say that your engine has, sounds to me that you've got a sheared flywheel key.This little piece of Aluminum is what keeps the ignition system in time"

Sorry, I meant by 'pop' that the engine was occasionally backfiring and igniting some fuel. The blade is firmly in place, it is not a matter of a loose blade, the engine itself does not seem to be able to compress the fuel/air mixture adequately.

The valve clearance is fine, and I am now starting to wonder if it may have to do with the piston seal.

What, exactly, were the valve clearances upon checking? Do you have a compression tester or, better yet, a leak-down tester? And it would be piston ring sealing not the piston and if you do, indeed, have ring wear, I'm not sure you should bother as this is a very inexpensive unit to replace and is usually cheaper to replace than repair.

I did not actually measure the clearances, but the valves were closing all the way. Unfortunately, I do not have a compression tester, but I can tell by how it feels when I rotate the starter that it is not able to compress the mixture.
As for the expense of repairing it, it doesn't really matter to me if the engine ends up working or not, as I have another mower that is running great. I have taken on this one as a project, and I am just trying to fix it because I enjoy working with small engines.