Might be as simple as a leaking head gasket or stuck valve. A direct replacement is no longer available from Briggs, the new engines are bulkier ohv's which may not fit easily. A dealer might have a suitable l-head in stock.

I checked the valves (took off head) and they do not appear to be sticking, nor do they look burned. The head gasket looked good also. It is getting spark, (tested), but there is just no compression. I am assuming these little briggs engines had no form of compression release for pull-starting. I couldn't see any evidence of such. I think the rings are shot...have never completely disassembled an engine before, but I may try.

Rings don't fail on the spur of the moment unless one broke, the evidence would be on the cylinder wall. That engine does have a compression release, if you turn the engine by hand you should see the intake valve move off the seat momentarily on the compression stroke.
The face of the exhaust valve may be corroded, you will not see that unless you remove the valve.

Yes, I know rings don't fail "on the spur of the moment". The mower was recently purchased used, and this is the first time I have attempted to clean it up and try to start it. I have no idea how many hours the engine has on it, or when it ran last. You know sellers, how they are: "Well, it was running". The spark plug had minimal carbon build-up, so appears to be fairly recent, but the flywheel and magneto was very rusty, had to wire brush all that, but it gives a good spark when testing with spark plug out of cylinder, touching motor casting. I even tried starting fluid (WD-40) thinking the carb (even though I disassembled and cleaned) might not be working, but nope. This engine has the pointless type coil.

I guess what I need to ask is, are "most" of the older Briggs engines of this type (vertical cylinder) standard, as far as shaft size for power take off? and base mounting bolts? I probably could find another 3.5hp (guessing at size).

You need to post the Model, Type, and Serial number of the engine, so we know what we're talking about.

The basic short block of the little Briggs 60000/80000/90000 series horizontal shaft has changed little in since the early 1960's. However, carburetors and other accessories have changed dramatically.

KOL will be somewhat fussy, because they usually have strap from the handles to the engine, and this won't clear the larger paper air filters, nor will this work with the latest B&S flat heads, which have a float carb and the tannk mounted above the carb at the rear of the engine.

Lastly, "no compression" suggests a valve issue, not rings. Even a broken ring will exhibit some compression, when cranked at speed.

Suggest you pull head and valves, clean valves on a wire wheel, and reassemble, checking for cleanances of .006 IN and .008 EX with piston 1/4" past TDC. If you don't have enough clearance, which is common on intake valve, you need to gently grind the stem until you achieve .004-.006. Don't be heavy handed, because if you remove too much, you'll either have to buy a new valve, or have the seat sunk by a machine shop.

I'm not familiar with this brand, but how old is it?
You can tell the engine age from the CODE on the engine label plate.
YYMMDDzz

My neighbor had a Toro reel mower that was from the 50's,. Her engine had reached the point of not starting because of minimal compression. It was simply worn out!