Here is the part #: TRANSUD0012 POWER TRANSFORMER  for MG50.

Contact a Marshall distributor and ask if they can get one.

Quote: "Do you think I can just leave the 3rd wire disconnected?".

Again. The third wire is used by the laptop computer itself.

If you simply want to use the supply as an external supply then the third wire is not used.

The 3rd wire is an identifying wire for the laptop.

We;; that was a big help.

I would recommend 'grounding' the clean channel wiper.
That should kill the signal.
As yet, I have seen no resistance measurements of the circuit.
I would look at the junction of C49 & C 22 to ground.
What are the readings when the clean volume control is swept from min to max?

So here is a pic of a 220 volt wiring.
Call the Blue wire tap #1.
#1 & 2 are one winding.
#4 & 6 are another winding.
For 220 V ac input the two windings are in series. (tap #2 & 4)
For 110 Vac input the coils should be in parallel.
So wire #1 to #4 and #2 to #6 .

Schematic:

That puppy was manufactured in 1977.
So any interboard connections are suspect (wipe them with DeOxit).
The controls & reverb jacks should also be gone over.
As to the squealing: do any controls affect it?
Be careful in there as there are quite a few obsolete transistors in it.
The slight distortion may be a bad speaker. Try another one.

Ibanez also uses a NuTube in the new Tube Screamer.

The 'Bright' capacitor C41 is 680 pf.
You could try a lower value, like 220pf.

I am stuck on the squirrely voltages on Q8.

Q8 according to the schematic:
B:Not specified (47K from ground, it's an NPN transistor so I would expect minimal Vdc)
C: +38Vdc
E: -1Vdc

Q12 should have a negative voltage on the base: 0.6Vdc

(You do have the schematic don't you?
The expected static voltages are well marked.

Not too sure what you are seeing.

Reverb output ic looks good but Q8 base looks bad.
That makes no sense unless Q8 is toast.

Q10 should have +49 Vdc on it.
Q11 should have +1.2 Vdc on it.
Which leads me to believe Q10 is bad.

You have more problems here than I think you can solve on a forum.

What does the signal look like at the base of Q8?
Q10?
Q11?
Q12?
Take care that the specified 250mv AC signal into Q8 is NOT exceeded.

What does "Q8 is irregular pattern" this mean?