Little Help With Mostly Dead Soldier

The Marantz SR 7000 quit last night, mid-movie. Complete shutdown for no apparent reason, then nothing. Try all the obvious stuff, nothing. Unhook everything from the back of it and, as I’m taking it off the rack, it turns on. (Yep, unplugged the wrong one. Damn rats nest.) So, I put it back on the rack and it turn off again….

Obviously, there’s just something loose in there – something I’m hoping I can find and fix myself. Pretty reliably, lay it flat and it turns off. Put it on its side, it’ll turn on. I’m hoping it’ll be something as obvious as a loose connection to the power supply, but I’ve never poked around inside it before – any guesses or ideas what I should be looking for?

Many thanks, and I promise to unplug it first this time. Honest.
I have no knowledge of this piece of equipment, but in a general sense I have a couple of ideas that might help if the problem is a mechanical contact. Take the bottom and/or top cover off. Then go through the motions that make the unit work in a dark room while watching the circuitry. If you are lucky the bad contact will be identified by a small spark as it makes contact. If this doesn't identify the problem you could try tapping various parts of the circuit with a non-conductive item like a pencil eraser. The bad connection should make/break contact when it is tapped by the non-conductive item.
Humm.... Wish me luck. Hopefully I can spot a likely culprit with the thing unplugged and the lights on, but we shall see.
Little more info, in case anyone out there has more experience with this stuff than I (which is to say, any at all) and would like to help.

Power up on the thing (when working) is accompanied by an initial, mechanical-sounding, click, followed a couple of seconds later by another one. The intial one appears to emanate from the vicinity of a roughly 1 x 1 inch box screwed to the board in the circuit path that appears to be directly between the power cord coming in and the transformer/power supply. I'm assuming it has to be some sort of soft-start circuit or manifestation of the actual power switch on the front of the box? The second click comes from roghly the other side of the chasis near the speaker taps.

Reason for the painful discription is, when this thing spontaneously shuts on and off, it's because that first clicking box just clicks on its own. It is extremely motion sensitive. Once on, a slight tap on it would cause it to shut down. (When I say shut down, I mean the unit looses power completely. Normally, when "off" there is a standby type light indicating that the unit is receiving power. Anger the little box, you loose everything.). If you tilt the unit at all, it would turn back on again. Maddening.

Anyway, I tried this for a while last night, until it just stopped turning on at all any more. Now it seems to be all the way dead, not just mostly.

SO, it appears that I'm going to need professional help on this one, but, just for curiosity's sake, what the hell is that box? Balck on the sides, brownish on top, and there's a rectangular little "window," for lack of a better word, on one half of the top with what appears to be a coil of wire coated in a green plastic sheath stuffed inside. Clearly, I don't have a clue, but I'm getting closer....?
Well I'll be a monkey's uncle. Turns out the thing is still under warranty. Just gotta schlep it a few blocks to the spot I bought it (one of the few thing's I've actually purchased new) before March, and they'll take care of it.

Happy trails.