It's possible.
On the flyback you most likely have a B+ or some may call it a C+
since this source is derived from a tap on the fly back.
It's common to monitor one of these sources for a quick shut down,
because it covers the flyback area problem and supply going to it. How
ever, caps do go bad here and the ripple being seen could be just enough
to shut it down when the circuit gets loaded.
This is a good time to use your scope, if you have one. First you
test the gate signal to the MosFet you replaced. My guess is it should
be a PWM type signal and should vary when load varies. You want to see
what the duty cycle is. what I have done in the past to test for this is
to put a low load R on the output of the supply while I am watching
the scope to see if the duty system increases to maintain output. Of
course, you could also just simply watch the output with a DMM as you
alternate your external load R.
While you're probing around with the scope, see how clean the signal
is at the switching supply's output after rectification and filtering.
I've seen bad UF switching type diodes/rectifiers go bad, they test ok
with a meter but have slow recovery issues under operation. Make sure
you replace these types with equally fast units. A good indication of
this is one operating hot.. This is a good time for a hand held IR meter. :)
Next, check the Secondary supplies coming from the flyback for any
ripple around 15khz.. You shouldn't see much at all. if you do, it could
be bad caps or slow recovering diodes.
P.S.
since the original MosFet was shorted, have you checked to make
sure the switching transformer leads are well soldered in? This was a
common problem back then and depending where the lead was that had a
cracked joint, it could cause intermitting back EMF on the MosFet and
short it.
Also, you may want to test for the Drain voltage and signal via the
scope to make sure you are not getting any over voltages that look like
spikes.
That should give you enough to work on.
Jamie