Those monitors are great.
It's probably bad electrolytic capacitors. They go bad with age and will sometimes leak on the PC board, screwing with other components, causing corrosion, and shorting connections with their semi-conductive gunk. It's possibly bad solder joints as well.
If I were you, I'd take it apart yourself and probe around in there (with the power off, unplugged from the wall). Look for bad solder joints, loose connections, bad components, stains on the boards in there, etc. That way you'll pick up more clues.
There's not much danger to you if the unit is turned off and unplugged from the wall. The actual danger presented from being shocked by a charged CRT is vastly less than litigation-fearing how-to guides will tell you. It won't kill you -- still, you don't want any shocks going through your body (especially your heart) if you don't have to, just in case. Just avoid the
flyback transformer and the cable that runs from it to the CRT, and you'll be ok.
Once your inside, take some pictures for us if you see anything suspicious and report back.
