I work on test equipment and experimental equipment a lot, and am familiar
with high-voltage precautions, but have not worked on a TV in 15 years.
Accordingly, let me ask...

The patient is a Magnavox 25-inch color TV from 1995. It went dead while in
use the other day (no one was watching at that exact moment) and now shows
absolutely no sign of power.

Where the AC power comes in, there is a tiny fuse, which is not blown, but
it's something like 1/10 amp and can't possibly be the main power inlet for
the TV. There is also an Omron relay or circuit breaker (at a quick glance
I couldn't tell which).

What should I be looking for/at?

Thanks...