What is your background electronically?
Before poking around - you need to be given the "CRT's are dangerous and can kill you" warning, and urge you at least make sure you know how to properly discharge a CRT. That out of the way...
The first and foremost thing once you're discharged would be a visual inspection - can you verify that all components are in good physical order? Eliminate any risk of shorts etc. While it may not have moved, many things can and will cause issues. Debris, or buildup of carbon can cause shorts. Humidity can be enough to kill a monitor. Maybe you already have done a visual check, but it's something that is pretty simple and doesn't require too much in the way of specialized equipment.
Look for bulging or leaky caps, burnt spots on the board, crumbling resistors and anything that looks unhealthy and document anything you see. It may tell you more about the health of your monitor than just how to stop it from blowing.