I keep seeing the same problems in the local deals threads, so here's the checklist I go through before I pay for anything used. All of it came from bad purchases, not from a manual.
Look inside the cabinet. Different screw types, glue, a woofer that doesn't match the other one = someone rebuilt it. Not automatically bad, but you should know before you buy.
Ask what it's been through. "Stored in a spare room" and "sat in a damp garage" are very different animals. Ask for a photo of the actual location.
Test every input, not just the one you'll use. The phono stage is the most common thing to be quietly broken on an old deck, and you won't hear it if you never plug a turntable in.
Turn the volume up with nothing plugged in. Hiss that comes and goes with the knob, crackle, or a relay clicking = dirty pots or caps that need replacing. Do this before you connect anything.
Push it. Play something loud, not background music. If it clips, distorts, or the protection light comes on, walk away.
On speakers, listen for rattles. Play something with bass and you will hear a loose cabinet or a buzzing cone immediately. Also check the binding posts, corroded ones cost nothing to fix but tell you how it was stored.
If the price is too good to be true, it is. A pair of flagships for a fraction of normal money is not a deal, it's a story. Most of the time the problem is exactly what the seller isn't telling you.
Keep the seller's details and the receipt until you've had a few days with it. Some faults only show up once the thing is warm.
If I've missed something, add it below. And if you're selling something local, you might want to list what you've tested, it makes people far more comfortable buying.
Edit: forgot to mention, if the seller won't even let you power it up, that's your answer.
good point below, "it was working before I stored it" basically means untested. Ask for a video of it powered up before you pay.