No, if you already tested it, don't go back out.
But it doesn't make any sense. If there is no power out, it can't start thte angle grinder, and just plugging a load in and turning it on does not produce a magnetic field - it takes outside interference for that.
Just from what you are describing, I would have to say that the capacitor is bad.
It is not allowing full flux to build up to create the magnetic field.
I just can't imagine how an angle grinder can create flux if it is not turning.
What I would recommend at this point is to take the capacitor out of the non running unit, and put it in the running unit.
Or take the carb from the running unit, and put it in the non running unit, if you know the generator end is good.