First thing to check on vintage equipment is ALWAYS the RIFA capacitor. When they fail, they pop, fizzle and smoke, and they're connected straight to the mains input wires so they usually take out the fuse when they go, too. If the RIFA wasn't the problem, take it out and replace it anyway (it will work without it too). It WILL fail eventually if you leave it in, and I've seen some pictures and movies of big messes caused by failing RIFAs.
I've never seen a CRT go bad from age (though I heard that early color tubes had phosphors that would eventually fade but that's not applicable here anyway). If the monitor section fails, it's usually the horizontal or vertical sweep generator, and in equipment of this age (before 1990 or so) it's usually a transistor that goes bad, not capacitors (because around 1990 manufacturers started messing with the formulations of insulation chemicals in capacitors). I don't think the 8032 has tantalum caps, those are usually the first suspects in equipment this old.
It should be fairly safe to plug it in and turn it on. Even if something is broken in the monitor section, it's unlikely to take something else with it that can't be repaired. Turn the brightness up a bit too so you can see if the circuitry is generating a picture (the brightness potmeter gets dirty so you may have to wiggle it a bit to assure good contact). The 8032 uses a CRT controller which has to be initialized by the 6502. If the 6502 doesn't run, the motherboard won't generate sync signals and the monitor won't show a picture (it's probably designed so that the blanking is active to prevent the beam from burning a spot in your tube). There are schematics and products to get a regular video signal from a CBM computer that you can plug into an NTSC monitor (or if anyone is reading this in PAL land: a PAL monitor -- European CBMs refresh the picture at 50Hz, American ones run at 60Hz).
If it turns out that the problem is indeed in the monitor, there is lots of information on the Web about what to do and what not. There are YouTube movies showing how to discharge a CRT. The CRT itself is what holds the charge: it works like a Leyden flask, so there's not some sort of huge capacitor that holds the voltage or something. If you want to work on the electronics, pull the PCB out (after discharging and disconnecting the CRT), and leave the CRT in the case. That's really the safest place for a CRT to be: mounted in the monitor. Moving it around for no reason just increases the risk that you hit it in just the wrong spot and break it. The place where the neck attaches to the bottle is the weak spot.
Check the bottom of the circuit board for cold solder connections, especially the line transformer (it doesn't hurt to just warm all its pins up to melt the solder; this is the most common place in all CRT TV's and monitors to have cold solder welds, because the line transformer is so big and jiggles around while the PCB is pulled through a soldering machine. While the PCB is outside the monitor, it's easy and safe to spot-check parts. If you feel uncomfortable, use an insulated wire to short out the part you're going to test for a few seconds. It's easy to desolder transistors (don't get them too hot) and measure them with a diode meter.
Check Zimmers for the schematic (make absolutely sure it matches your system of course). Monochrome CRT monitors with separated sync inputs are not very complicated and you'd be surprised how much of the circuit runs at relatively safe voltages to poke around, even when it's connected. Of course if you don't have a steady hand, or don't trust yourself not to touch a dangerous part while you're checking a plugged in monitor PCB, you shouldn't even get started.
But first, make sure the motherboard is okay. Without a working motherboard, the monitor won't do anything even if it works perfectly fine.
Check out
Tynemouth for important tools to help you if there's anything wrong with the motherboard.
===Jac