amp I bought 3 days ago not powering on - electrical engineer advice wanted

excellent diagnosis @devinplombier !

I baked some pastry for you to come over and look at it. But you did it remotely.

I read those steps a few days ago and didn’t solve it.

One more clue:

When I turn it on, and it does not work, in about 8-10 sec, the volume dial’s light turns on and makes a popping sound, sends a signal to the speakers. When it works,  the source selector light comes on (the first of six - phono), and it takes the same time for the dial to lit up but no pop sound. 

What it does not turn on, the selector does not light up. So obviously, the power does not go to the sources, the relay cuts it?

I tried  the mute on the remote. Replaced the batteries. Does not work at all.

Most sites on line where you purchase used components will make the seller take it back if was advertised is working condition which apparently it is not. Message seller and tell them what happened. Stick with it. Over the years I've returned 10-15 components that didn't work right mostly from eBay.

@zx10 right. But craigslist, paid with cash?

When I turn it on, and it does not work, in about 8-10 sec, the volume dial’s light turns on and makes a popping sound

@parkergetdean you mean the speakers make a popping sound?

I don't know, the intermittent nature of the fault kind of makes me think the issue might be with the protection circuit / relay. DC offset issues (which would trigger protection mode) don't usually come and go.

Just totally uneducated guesses on my part about an amp that's 1,000 miles away, I'm afraid. Thank you for the pastry offer!

All these people suggesting returning the item should give that a second thought.

I'm not sure how many times the OP used the amp before it quit, but he says "played it every day, worked fine".

So let's just assume that means a week. Are you seriously saying that if a piece of equipment you sold breaks down in a week, you are on the hook for it? It's a used amp, and I'm guessing it's at least 20 years old. To me the typical bar for used sales is that it works out of the box. Or at least it doesn't break during the first or second use. What is the implied warranty on a used item if not specified at the time of sale?

He can go back to the seller and ask for compensation, or whatever he's willing to do. But I don't think he's on the hook for it.