Ok, thanks Rob. I had a feeling this wasn't good. I did reinstall the known-good 6HE5 back into the roundie, and it's OK.
Now comes the part where I have to admit I'm not an electronics expert. (In case you didn't guess)
How do I test the capacitor? I'm assuming it'll be located under the chassis, somewhere in the vertical section. I also have a schematic for this set (and most other Zeniths, thanks Ebay).
If it's bad, where do I get a new one???