[morzh]

OK.

If the chassis is in bad shape:

1. Cut the power cord. Better yet, just unsolder it from where it goes to, and solder a temporary one, whatever it is. I never check for short/open, but you might: use a DMM on Ohms, put across the power plug.
Note: do not hold with both hands: you might receive a mild, but unpleasant jolt, even from DMM.
See if the number shown is reasonable: many tens to a couple hundreds of Ohms.
2. As Chas suggested, remove the rectifier. And all other tubes as well.
3. Insert your power plug to your Variac (turned OFF) output. I never suggest using "dim wit tester", it is a bad way to test things.
4. Set your Variac to Zero.
5. Insert your DMM (meter) leads into the Rectifier tube socket's pins that are the High-Volt pins (slim ones).
6. Turn on your variac, and gradually increase the voltage. Notice the DMM showing the value. If it shows nothing, see if your connection is OK. If it is, unplug everything and check both the In and Out windings for short/open. If you see the voltage rising and nothing smoking, proceed to 110VAC; your DMM voltage now should be about 600VAC. If it is: turn the Variac OFF (keep the 110V setting).
7. do the same procedure but now put the leads into the fat pins contacts. After the Variac turn-on, You should have either 5V or 6.3V, depending on what tube is used for the rectifier.