Briggs and Stratton Generator with Nikki Carb Gasket Issue

Bought a Murray with a 4.5Q Briggs and Stratton motor on it. Non propelled. I am at work at the moment and can supply all model / SN when I get home. The Problem: Previous owner mentioned the lawn mower had been turned over, upside-down. Mower will start, however bogs down, chugs, rough idle, smokes little to none... occasionally shutting off completely. Spark plug quickly becomes dry fouled with good bit of dark black carbon build up. What I've Done: Drained oil Drained gas Cleaned air filter Carb cleaner on carb, gas tank, spark plug port New oil New gas New spark plug Unfortunately for me at about midnight last night.. cranked it up and got very similar results. At first the primer didn't even want to prime, then it started eventually. Spark plug quickly got the dark black build up... and mower just still idled very rough. I have pictures, and video and like I said will have SN's when I get home. Next I was thinking of replacing diaphragm... but after that it is kind of beyond my scope of what's next. Hoping to learn some new tricks here. Thanks in advance for anyone who takes the time to help me..... I am sure I am breaking some rules, and especially by not having the exact numbers, but hoping to have something to do tonight to get it running maybe, and if I need to buy some parts.... before it gets too late.

I have a Briggs Model : 445-677; Type 0413-E1 in a Yardman riding lawnmower. I had a hard time getting the mower to start. I had to charge the battery every time I wanted to mow the lawn, so I replaced the battery with a Diehard 340cca. First couple of starts went great. Then I turned off the mower and went to restart and the flywheel traveled slightly and then stopped. The starter engaged, and the engine "chirped", but didn't crank. If I turn the flywheel a 1/4 turn, then crank again, it starts right up. I put a volt meter on the battery and with the engine not running, it measures 12.5volts. With the engine running it measures 13.5volts. When the engine doesn't want to turn over when attempting to start, the voltage drops down to 10volts. Any suggestions on what is going on here?