This is probably one of Dave's most informative videos. It demonstrates that you need to be systematic about troubleshooting.
Anyone who's fixed anything fast knows the feeling of adoration when we take a guess, replace a part, and everything works—but that's kind of toxic. It makes us lazy.
Dave proposed a hypothesis then tested it based on the criteria. The resistance to abandon the theory was palpable in the video—the primary-side problems seemed so promising. But when it failed to manifest when testing the unregulated voltages. Then the hypothesis that there was a downstream problem with the horiz./vert. boards was also promising, but it too was dispelled when it wasn't an over-current problem.
The thing I take away from this is, "don't guess" or at least "don't take your guesses on faith." Divide the problem somewhere—the power supply is a good start: "is the power supply output okay?" If no, then you can start troubleshooting the power supply. Divide at another point: "is the transformer output good?", then another point, "is the unregulated power good?" ... and at any point you've narrowed it down to "point A is good" and "point B is bad" so you can figure there's a problem between point A and point B.
Another thing—this also from just getting older and less cocky—if there is troubleshooting information, follow it. I say "from just getting older" because when I was younger, I'd think "why do are we doing things the hard way? we can skip this and that..." but now I know enough to recognize when someone is more experienced than I, and to just do what I'm told until I understand why it's done that way. Troubleshooting information just might be written by someone with more experience than you—particularly with what you're currently working on. So use it until you hit a dead-end.