Circling back on this one. Full disclosure. So, I was struggling with the no start problem again. After going through EVERYTHING (including gas tank removal/cleaning, new fuel lines, new fuel pump, plugs, valve adjustment, etc. etc. etc.) I began to zero in on the carb. What did I find? THE FUEL SOLENOID WAS WORNOUT/INOPERABLE. So, I had to make a decision. The OEM Briggs replacement fuel solenoid is $147. The knockoff replacement carb WITH a new fuel solenoid is $33 with free shipping. What would you do? I bought the knockoff carb off Amazon and put it on. It was SIMPLE and the Briggs started instantly. Engine ran PERFECT right out of the box. Yea!!
For at least two decades I have been saying that the little anti backfire solenoid or after run solenoid or whatever you want to call that car solenoid is the most overpriced part on a lawn mower!
They were only 68 to 89 a few years ago and they were not available in the aftermarket at all.
Then, all of a sudden a few years ago they popped on eBay and then later Amazon coming with the carburetors but also by themselves for $7.95 to 10.95.
They are designed for two purposes that I know of. They act like it's to prevent them from popping after you shut off the engine but about 80% of the time they fail to even do that because many of these mowers with an operational solenoid will still pop quite often when you shut them off.
Then the second reason I think is the EPA really wants them to be on there because they don't want that fuel being unburned and going into the muffler and basically the air when you turn off your engine.
You'll find a good deal of them that have been snipped off with a pair of wire cutters and the engines are really no more likely to pop when you shut them off then before because like I said tons of them don't do their job anyways.
Kohler even issued a TSB for the after run pop or backfire as some people call it but it's not really a backfire, and it said to idle down the engine to your slow idle speed for 30 seconds before shutting it off..
I usually just add them down for about 8 or 10 seconds and that does the trick.
But yes.. that is the one I would buy too, the only problem here is this has been a gigantic thread and you've revisited multiple things multiple times to finally get back to the fact that it was not getting enough fuel as everyone said from the beginning.
Between 80 and 95% of the time plus every time you have a running issue or no start issue it boils down to that same thing that you're not getting enough fuel.
In the future remember that you can usually test that part by turning the key on and off and listening to it click or leaving the key on and hooking the wire to it on and off to see if it retracts but sometimes they will also get hot and break down so one way especially on those that will run a while and then stall out is to simply unscrew it and hold your finger on the bowl and hold the bowl on for a few seconds to see if it keeps running. If it does you know it's the solenoid.
It's down there impossible to find a bolt at the hardware store that will hold one of the bowls on to replace the solenoid but if you have a large selection of old carburetors you can usually find one or you have to basically get a bolt and a gasket and cut the bolt threads off shorter and smooth them out which I really don't recommend. Just take an old solenoid and snip off the end.