[Arran]

Finally got started with some tests today. I had to get a laptop set up at my work station with proper files running in the proper programs.

The first four tests (power transformer) are done and already I am literally aground.
1. 37.7 ohms
2. no reading
3. no reading
4. no reading

Now I know why the power cord was cut.

Looks as if I will be looking for a transformer right off the git go. Any suggestions?

 The power cord was probably cut because the rubber insulation was rotten and flaking off, before you write off the transformer it would be best to double check things. The power transformers on those sets have a metal box covering them, the box should unscrew or unbolt from the chassis to expose the transformer itself, if it's burned out it will show with globs of melted wax and tar, not to mention stink. I find the infinite resistance readings suspect, there should be a primary winding and two secondary windings, one for tube heaters which is low resistance, and a high voltage winding which has three leads going to it and a resistance of maybe a few hundred ohms. That 37.7 ohm reading sounds like it may have been the primary winding.
 To test the high voltage secondary pull the #84 tube, find out which pins connect to the plates, and stick your Ohm meter probes in the applicable holes. Then find the center tap for the H.V winding, usaully either connected to the chassis or to a large wire wound resistor and measure between each of the plate pins and the center tap, the resistances between the center tap and each plate pin should be close to equal (in truth you can measure between the chassis and those two points even with the resistor in series, if the resistor is still good that is) For the tube heater winding stick the probes in the two socket holes for the fat pins of either the #84 or the #41 tubes.
Regards
Arran