Something is demagnetising the rotor. If a load is present, then that can do it... but you have no load.
Unloaded..and generating it's 110 or 220 whatever, does the motor sound laboured in any way. I'm wondering if there is a short on the 12v line (diodes?) perhaps.
There is something causing the demag.... or the RPM are not high enough (check frequency, not just voltage).
Try over revving it when it starts and see if that causes it to energise, or bigger cap for a test..... maybe open circuit on the rotor still ( other one you didn't fix). Usually if the rotor has an open on one side/or short, it can still work... but very poor regulation.... all over the place.... but it would be a bit of a coincidence if both went at the same time.
As I understand it, it is supposed to work like this.
When started, the rotor with it's residual mag, starts to generate a small voltage, which is generated in the cap field and the output.
The current in the cap sloshes back and forward between the cap and the coil... this current flow gets stronger, and influences the rotor windings, which is shorted in one direction by the diodes, and so becomes an electromagnet with constant pole orientation.
The whole lot starts to get more current flowing in the rotor, and then very rapidly it builds to full power. The resonance between the coil and the cap keeps the rotor voltage up, as does the current now flowing in the main field. The more current you draw from it, the more magnetic field it projects back into the rotor winding, so in theory it self regulates.
Now if this isn't happening ... why not.
Any load on the output while starting will kill off the cap/coil build up.... by bleeding the voltage away from the tank circuit
Any internal shorting in the cap will do the same.
A short on the dc output will probably be enough to stop it... although this only affects a small part of the primary, or it's own winding (build dependent)... and something should be getting hot.
An open circuit in the cap coil may not stop it running if the main coil can provide the magnetic field to the rotor... but would require some loading on the main field to make a current..
I'm running out of ideas here....
So check the resistance of the cap field, and the run field and the two rotor fields.
Check for shorts to ground in all the coils, I have seen cap coils shorted to ground near the start of the winding, which didn't generate much heat, but as they usually ground one side of the main, then it can be a problem.... auto transformer effect in the cap coil...
Nope... I'm done
all else fails...a push button flash switch
)
.................oztules
Edit just saw Dang post..... dose not work very well like that I would think, as the coil resistance is fairly high, and will limit your "big spark" to only a few amps... not enough to terrify the rotor I suspect.... never tried it though.
Manufacturer states to do it when running for a reason I figure .