The PDI doesn't care about GFCI so it wouldn't do anything about it.
Sounds like your converter has failed. A loose connection isn't going to cause a GF unless a wire is completley disconnected and touching ground someplace.
The converter might cause the GFCI to trip IF it's powered by it and the stereo could be affected by excessive ripple on the 12V circuit.
Do these items behave with the converter disconnected (not just having the breaker off)?
FWIW, flipping a breaker wont always isolate a ground fault even though it seems to have done so in this case.