[Hammarlund] TX-500 problem

[Charles Ochs]

"They can stab it with their steely knives, but they just can't kill the beast"
Eagles-Hotel California

You have NOT checked that power transformer properly!
Put an AMMETER in series with the AC line, NOT a light bulb! A light bulb will add just enough series resistance to camouflage the problem, and it takes a certain amount of current to cause any visual indication.  A very crude method, at best.
DO measure the voltages out of the various windings with ALL loads removed. Yes, this requires dis-connecting everything downstream, but you MUST completely isolate the windings for a proper measurement. 
DO use a variac. If you do not have one, GET ONE! Run the input to the transformer at exactly 120 volts. Hang a good DVM across the variac output to confirm this. 
THEN-measure the outputs from the windings. I assume that you have the service manual, if not, GET IT! This will tell you what the HV should be. 
Than measure the LV windings, Always allow "room" for no load / full load. For example, your 6,3 volt winding will measure something close to 7 volts. A 5 volt winding may go over 6 volts. Experience is the teacher here. The higher the normal current drain under load, the higher the no-load voltage will be. If these readings are LOW, you have a problem with that transformer, Houston!
And-last, but certainly not least-a transformer with a couple of shorted primary turns will HEAT UP--even with no load. After a few minutes, you will know! You will be able to feel it, smell it, or even hear it. Watch the ammeter!!
I know full well that the last thing that any restorer wants to know is that the transformer is toasted. It's the thing we all dread, but the sooner you confirm it's condition, and move on to find the real problem, the less time out of your life that you will waste.
Chuck
N1LNH
"Been there, done that" more than a few times!