Per von Zweigbergk ) writes:

The component was connected in series with one of the AC power inputs,
and measuring over the poles gives me 0 Ohm of resistance.

You need to get the terminology right.

"0 ohms" is a short. SOmething in that location with two terminals and
shorted is unlikely to affect operation. If it's really zero ohms, then
it will pass the current and everything will be fine.

If you actually mean "there's no ohms across it" then you really mean
it has near infinite resistance, ie an open circuit. If that's the
case, it's no wonder the rest of the thing doesn't work, it can't get
power since this open device is preventing any power to get to the
rest of the device.

On the other hand, even if it is open, chances are good it's not a
particularly special device, though it is there to protect the rest
of the circuit, either a fuse or something to limit current when things
get turned on initially. It won't work without something there, but
what it does is preventative.

If it really is open circuit, then you have to consider that it may
not be the fault, but a symptom. If it's opened up, it might just
have "worn out" but it may have "blown" because something else in
the unit is bad, causing this component to go with it. Until
you determine whether there is something else at fault, replacing
this component may merely mean it "blows" again.

On the other hand, it may be that simple, replacing it does fix
the problem.

Michael