Can I use this working one to somehow determine what may failed in the broken one?
Yes you can
draw a concise list os parts with locations and references
Measure the voltages at proper KEY POINTS
(deciding what is a key point is your great challenge)
BE VERY CAREFUL BECAUSE SOME POINTS MAY HAVE about 1KV (spikes)
** DO NOT MEASURE THE SWITCH or FLYBACK PRIMARY DIRECTLY **
it will damage your instrument quite easily
that said you have the secondary and the IC voltages
w/ care about the primary pulses...
take note and dup the procedure on the failed unit
with some luck you may have a very good start point clue or direction
Paul