The starting capacitor is used to start the hood vent fan motor. It's also called the hood capacitor.
On page 8 of the document you refer to above, on figure O-1, you will find the hood capacitor. It is shown on the control unit (circuit board). I've attached a snapshot of that area below.
Its leads connect to terminals A1 and A3. The hood fan red wire goes to A1, and the yellow wire goes to A3.
That part is not shown in this document as a separate part, so you will have to get it generically from an appliance parts store or electronics supplier, but you will have to order it by value.
You need to look on it and it will say something similar to this:
"7 uF 230V". In this example, that would be a 7 microfarad, 230 volt capacitor.
It's okay to get a capacitor with a little higher voltage rating, but not lower.
The capacitor, if truly bad, may not look bad. It can be quick-checked with an ohmmeter to see if it will charge and discharge (the meter will first indicate low resistance then go high to infinity). This is not a full-blown test, but for this kind of capacitor it may be enough.
You should check the solder connections, also. It's a large part, and sometimes they don't get enough solder on them. The connection may be cracked and just need to be resoldered.
Since a new thread was started, it makes it harder to follow along the saga...
But this problem could be a bad (or jammed or obstructed) hood fan motor, a flaky relay on the control board, a bad cap, or bad wiring.
Microwave hood fan motor starting capacitors usually look something like this, and may be red, blue, green, orange, etc.