An update on the situation - the monitor he was using was a composite
color monitor for an Apple //c. He said that the screen got real
bright, then went black. I had him start it up while I was there, and
the power light on the monitor didn't come on. I'm hoping this just
means I have to replace a fuse, but I'm not sure.
Given the number of high-voltage components in a monitor, I wouldn't
try to mess with anything other than a fuse unless you really know what
you're doing and have experience with TV repair and the like.
Otherwise, if it isn't a fuse then you're better off replacing the
monitor given its age, most likely way-exceeded duty cycle, and cost to
repair vs. replace.
You can probably find a cheap composite monitor at a goodwill or
salvation army for next to nothing. I picked up a Commodore 1040 for
$10 in great shape, beautiful bright picture and all. Absolute
worst-case you can always get a cheap TV from goodwill or a pawn shop
and a $15 RF-modulator box.