I mean absolutely no disrespect with this post, Pete, and I certainly hope you take none. However, there are components inside CRT monitors that retain a charge even long after they've been unplugged. A charge strong enough to kill a person.
I always recommend that if someone really wants to save their CRT for whatever reason, that they take it to someone who is trained and qualified to do so. The fact that you're actually asking how to locate the problem or repair a CRT (or to try to find the problem) would lead me to believe that you aren't trained and qualified to repair one. I understand that you apparently know a lot about electronics, but if you aren't completely familiar with how to service a CRT monitor, please don't attempt to.
If you must repair the monitor, please find someone trained and qualified to diagnose and repair the monitor.