Does this thing have a "clock" style hour meter? Or a digit style? I'm seriously doubting those hours. Not that a small engine couldn't last that long, but that Briggs I/C is known to pop valve seats at or around 1000-1500 hours. I've not seen many Kohlers make it to 3K, let alone 3600. I'm thinking that the hour meter is incorrect, or the engine has been replaced, or both. How many acres has this thing mown on average? Sorry to be skeptical, but if your engine is in fact original, and it does have 3600 hours on it, keep running it and when it blows, call Briggs and Stratton and tell them how many hours you have on it.
At this point in the game, I would try and fix it. If it lost power so suddenly, it could have dropped a seat, but not if it will start on both cylinders one at a time. The fuel pump diaphragm may have let go. It is an odd fuel pump, mounted to the carb and vacuum operated.
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