My wife turned on the wall switch and the pendant light over our dining room table went out. The fuse outside didn’t blow—none of them needed to be reset. I checked for power in the light’s hanging cord, but nothing. I pulled the wall switch to check for power and nothing there either. Thoughts?
If there is no power to the switch and the breaker didn't trip there is likely a switch with GFCI on the mix.
Another possibility could be a bad breaker (assuming you don't have actual fuses), check this by flipping the breaker off and back on. This could also help to identify other lights/outlets on the circuit. If there is a wiring problem, knowing what other devices are on the circuit could help you track the problem.
While not impossible, it is unlikely that a wire has been severed. It is possible that a wire came loose at another outlet or fixture in the circuit.
If there was a true short, the breaker would be tripped out fuse blown and it would continue to trip.
I always encourage people to do an audit of what is on every breaker when they get a new home (and make notes). It takes a little while, but when something like this happens, you know exactly where to look. It's harder to diagnose if you don't know what breaker the fixture is on.
Agree on the GFCI advice. I had that happen - the GFCI outside tripped and took out half of the lights in my kitchen. Whoever wired them put them electrically downstream of the GFCI. Took me days to figure out what was going on, because it didn't occur to me that the outside GFCI would be protecting my kitchen lights. And I wasn't trying to use the outside outlet for anything, so I didn't notice it was out.
By "fuse" do you mean "circuit breaker?"
What do you mean by checked for power, are you saying you put a multimeter on the light's cord and the light switch, with the circuit energized, and aren't getting any signs of electricity?
Since you said you aren't getting power to the bulb at all with the switch on. I would start by killing power via the circuit breaker, unscrewing the cover of the switch and checking the continuity between the two powered terminals on the switch using a multi-meter. It should read continuous when on, not when off.
If that test passes, check for GFCI outlets on the same circuit, see if any of them are tripped. A GFCI outlet, when properly wired, will protect an entire circuit and cut power to it.