Briggs starting issue

To start I have a 31p777-1076 briggs intek ohv. I am currently having an issue starting the unit. It started acting up about an hour into mowing, when the mower starting running rough and blew a single puff of black smoke, ran a little rougher and stalled. I pulled the plug and found it to be fouled, At this point I proceeded to do some maintenance as the mower was new to me (came with house). I changed the plug and the fuel filter, blew out all of the grass clippings from the fins(and replaced flywheel fan as I screwed up and mangled it reinstalling engine cover...rookie move on my part). I tried starting but it continued to run rough and stall. I then found the exhaust valve flapping in the breeze, and did the proper adjustment to .005. The battery is good and I have even tried jumping the starter but I only get 1-1-1/2 turns from flywheel and the starter bendix stays engaged to flywheel ring gear.:confused2::confused2::confused2:
Any Thoughts?

CF

double check the inlet valve.
If the gap is too big the decompressor will not work and the starter does not have the balls to turn over the engine.

Your symptoms however sound very much like a blown head gasket.

Thanks for the info
I will try the valve adjustment again , but if all else fails it's going to the shop. I haven't got the time or experience to tackle a head gasket.

So! Went back to the drawing board!?!? Turns out the stem cap had come off the valve. Made all of the necessary adjustments and away she went. Cut for over 2 hours and not an issue. Thanks to everyone for their assistance....glad it wasn't anything more serious.