I hear ya. Well nozzle and filter should be changed once a season in my book. if you loosen the screw (s) and unhinge the transformer (coil) naturally after shutting the service switch or breaker off, you should see a round short tube, generally 2 yellow wires, that is the optical flame sensor.
naturally its lens should be somewhat clean so as to "see" the flame. if some water made it thru the filter and got in the nozzle and caused the spray of fuel to "pee" a straight stream thus causing the flame front to burn badly, smokey,black, then that flame devise would have noticed and shut off the burner.
now with that said, that why the nozzle and filter get changed first by a tech. now here is the part where he turns it on and it works and walla.... bill and leave.
experience repairing any thing is as important as quality dependable tools and equiptment used to diagonois and repair AND the ability to digest gathered info,process it, and use it for a confident repair.
Where is the unit located?? town... the noisy aquastat is my first raised eyebrow thing to look at. a contactor relay sitting there buzzing would cause me to look at and clean the points of the contactor if they are dirty or burned. then ifso facto replace it. you got a pic of the burner? is it a afg model?