A couple of years ago, I was passing by the trash bins at a local computer repair shop. Atop one of the bins, there was a National NC-60, in good condition but slightly moist.

I took it home the next day and inspected it, and everything seems to be in decent condition - albeit a little dirty. But after three years of having it sit on a shelf, I've never even tested if it works or not!

I had someone mention that the power supply caps might be bad. What should I expect when firing up a 52-year-old radio?

Expect the electrolytic capacitors in the power supply (usually just two, often in the same can) to be shot, and needing replacement. The coupling capacitor to the audio output grid is suspect; best to replace that too.

Then plug it in and see what explodes. The NC-60 wasn't top of the line but could provide some entertainment with AM and even some SSB and CW.