What is the cause of rattling noise in the engine compartment? Nothing shows on the dashboard.

If the valve is stuck in the closed position, Yes it can cause excess pressure through the engine. Is the engine doing anything else different? The valves are usually quite cheap to buy and fairly easy to replace so it could be worth replacing it anyway. Do you have any warning lights on the dashboard?
A quick test is to remove the PCV valve from the engine and listen to it as you shake it. A working valve usually has a Rattle sound. No rattle suggests a stuck valve. Some valves can be cleaned but this is usually a short term fix or to get the vehicle home.
A stuck valve can cause a 'whistling' noise from the engine and it can also cause the engine oil to become sludge. If you replace the valve It could be a good idea to do a full oil AND filter change as well.

Do you think the sound originates within the passenger compartment or possibly from within the engine compartment? There is not much that might knock inside the car . If it knocks every time you switch off I would suspect the engine compartment and a mechanical cause.
Might be something a loose component, maybe the exhaust hitting something as the slowing engine vibration causing a harmonic at a certain point. Possibly, but unlikely, an engine mounting.
Have somebody assist you to trace the source of the sound, it is hard to do alone.
There used to be an Audi advert in which a sound could not be traced and it took an expert to track it down. (He had to oil the pendants on the woman driver's earings!)

Then by the tone of your question your not
up to the task

Go to a repair shop & avoid the stress

Yours may be different but on my 2007 prius I found out that the rattling or clicking type noise came from the dash rubbing against another piece of plastic somewhere up by the windshield. I just lived with it.

I would check exhaust system for loose heat shields or bracket.

check for leaks

Our 09 developed a loud rattle up toward the windshield. Turned out to be the plastic "cowling" that the wipers sit in which runs the length of the engine compartment. I think some servicing requires the cowl's removal so maybe it wasn't reinstalled correctly. Open the hood and along the seam where this cowling attaches to metal trim below (via snap in plastic links), squeeze a thin bit of weather stripping. I actually used a couple of plastic hose nozzle washers in the gap as a test and the rattle disappeared!
Its a cheap and easy test in any case.

Does it only do it with the a/c on or does it do it with it off and in gear. If it does it with the air off and in gear the the problem is possibly in the tranny. If it only does it with the air on the possibly another pully in a bind causing the rattle possibly water pump.

Have you checked the catalytic converter (also reffered to as simply a Cat by mecanics)? It's the first big canister you encounter on the exhaust line right after the manifold and before the resonator and/or muffler. After a while rust and time can cause either the casing itself to come loose and rattle, or the insides themselves break up and rattle around the cat. And being where it is it often resonates sound around the engine compartment, making it seem the sound is coming from elsewhere than it actually is. And while your at it don't forget to check the flex pipe usually connected to the cat also (some models do not have a flex pipe though). If all that is fine, then the other things to check would be the accessory brackets, wire holders and the like. With vibration and time, sometimes they loosen up and start to rattle. Still nothing? check the suspension parts for anything loose (IE. sway bar links, coils springs, tie-rod, suspension tables). Other than that there isn't much in there that can rattle. If you look at how an engine is built, you'll see that there isn't much inside that can rattle around without causing the engine to fail altogether. I'm not saying it can't happen though, but it's highly improbable. Hope this helps

Check the heat shield on the catylitic converter,exhaust manifold. Kev-Mn