So far everyone says sayanora to this B&S. OTOH, it does not have the head gasket failure so common to the brand. The valves themself seem to have a lot of meat left on the seating area, and could be ground or lapped to improve compression. Need a picture of the valve seats built into the head for evaluation.
You should look at the installed height of the rocker arm mounting studs. They have been known to pull out of the head over time, sometimes made worse by overheating. If you have not checked, take a look down on the cylinder from above and make sure there's no clippings, etc that will block airflow over the fins, block and head both.
If you have low compression, check that the valves move freely in the valve guides. If sticky, that can make the valves hesitant to seat, causing low compression. They should slide in the guides freely, with no wobble of the valve tulip when the valve is open 1/4". A slight wobble is acceptable.
Not having any more information, I would clean the head gasket surfaces and use a new gasket to re-assemble the cylinder head, and then adjust the valve clearance.
If it does not have compression after cleaning up the valves, squirt some oil through the spark plug hole and re-check compression. If the rings are toast, oil will provide a temporary assist and compression should improve.
From the little I see, the valve seating area is not great, and the valve seats are not shown.
If you actually have no compression, and you have adjusted the valves, and they are not sticking in the guides, all that's left is the ring condition. Most times, rings will fail slowly over time, and will not suddenly cause a no-start. If the compression release built into the cam is stuck(or broken) it may hold the valve off its seat and cause no compression. B&S compression release is known to die and scatter parts throughout the crankcase with no warning and no particular reason(that I know of). That can explain a no-compression problem that came up instantly. Replacing the cam cures the problem in most cases. Bad ring sealing would also tend to cause the engine to feed oil to the carburetor leading to blue smoke when running. If you did not have blue smoke, most times your oil consumption would be low. If you have significant oil useage, rings are more likely.
tom