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The fill hose, that goes to the fill tube, was being kinked, when the reservoir lid was being placed on the tank.

After many weeks trouble shooting, and guessing, and asking for help, I am 90% sure I have solved it. I will leave it here, as a "quiz"

Tomorrow I will start giving hints. I got this...

OK, I have done some trouble shooting, and hopefully it helps

The toilet bolw sits 1/2 full, if I flush, it burps, fails to flush, but fills properly.
If I then flush it again immediately,...