Eddiie:
Ah yes the fuse was blown! It was also a 3 amp fuse, when the board calls for 2 amp. Another bad sign.
I have put a 2 amp fuse in, applied 110 volts AC to this board and nothing happened. The lights in the house dimmed for a split second while the current rushed in, the fuse did not blow. The light bulb did not light. The bulb is good.
One might worry about the lights flickering, but it suggests the bridge rectifier and capacitors are working.
Likely the transistors - one or both - are open circuit then.
Eddiie:
The replacement parts I ordered are everything on the board pretty much -
I am quite sure it would be cheaper - far cheaper - to buy a new module. Nevertheless ...
Eddiie:
the Diodes test OK. That is, I get nothing on the volt meter when probes connected one way, and something registers when reversing.
Sounds good.
Eddiie:
The last piece is the C5071 transistors, replaced!
I thought you could not find data on them? I am fascinated you could order them without knowing what they were.
Eddiie:
The transformer I would actually like to rewind if needed.
I doubt it.
Eddiie:
I think it would be a fun thing to do.
Messy.
Eddiie:
The parts are being replaced as they arrive. Therefore, pretty much everything will wind up being replaced and no need for the waste bin. Right?
But you will still have a number of old parts of dubious reliability.
Eddiie:
That is, the C5071 transistors I connected 12 volts DC was getting 12 on the volt meter. Maybe that is a direct short?
Not sure exactly how you are describing testing them.
Eddiie:
I noticed these transitors although connected to the frame for heatsinks they had protective material between them. Does this mean the backs are live and I should not touch? The replacements have a black backing and feel more plastic than metal, is this possible?
Some transistors have integral insulator, most do not. I would include it if it was previously there. Unlikely to have been damaged by the overload as such, but you need to be mechanically careful with it.
Eddiie:
Have not ordered the diodes, should I?
Don't know - haven't studied where they are involved in the circuit.
Eddiie:
Ok now this scares me.
It should.
Eddiie:
The freaking light bulb is only 24 volts!!! Perhaps this is a bust of energy to ignite the halogen gas on startup?
This thing is after all, a "transformer" and the bulb is a filament bulb, not a discharge tube.
In normal operation, each capacitor is charged to the peak of 110 volts, which is 154. Together they total 308. The two transistors chop this into a square wave whose peak-to-peak amplitude is 307, thus its amplitude from the middle is in fact 153 again. This is now fed into the transformer which "transforms" it down to 24 V. Note that what the bulb gets is high frequency AC - not DC.
Eddiie:
Understanding what you're saying and looking at the traces. With the link out (220 volt mode), only the bridge rectifier is active which adds 220uf to the other 220uf passing it on through to one C5071 transistor then my head starts to spin following what happens next.
In this mode, the two capacitors are in series so they share the 308 volts. The transistors "chop" alternately from one end of the capacitors to the other. The transformer is connected (through the polycaps I gather) to the midpoint of the 308 volts. The polycaps are (I gather) used as the electrolytics don't particularly like the high frequency current.
Eddiie:
When the link it together (110 volt mode), I still lose what happens. There is a trace from the N side of the AC input to the 220uf caps. Crazy stuff. I have note ventured too far into waves or clocks yet. Perhaps this is what I am missing and why it is not making sense. Thank you for your time and explanation.
With the link in place, one side of the supply is connected to the midpoint of the two caps. The other side charges one cap on the positive swing and the other on the negative, using only half of the diodes in the bridge; the other half just stays reverse biased. So each charges to 154 volts.
Eddiie:
Why are we at 308v now? That bulb is 24 volts! This 308v gets fed into the transformer? What is the purpose of the transformer then?
It transforms! 
Eddiie:
Why take such large inputs?
Because that's what the mains voltage is.
Eddiie:
Why step them up?
Because that is the peak of the sine wave. That's what happens when you charge a capacitor with a rectifier.
Eddiie:
How those big orange caps stop the transformer from seeing DC is something I'd like to learn I could use this idea in other things.
A capacitor in series prevents DC from flowing.