Recommendation for an Ultra-Quiet/Silent CPU Cooler and PC Case?

[QuebecActual]

Hi all, I'm rebuilding my media PC to use for gaming and I would like some recommendations for an ultra-quiet/silent CPU cooler for my Intel i5-4690k.

I'm in a tight spot because I need an air or closed loop/AIO cooler that is more quiet than powerful, but still powerful enough to cool a potential overclock of 4.4 GHz on the i5.
I'm also looking for a PC case that is cube shaped (or low in height), supports a full atx motherboard, and includes sound-dampening material (for soundproofing).

I will be playing games like Mirror's Edge: Catalyst, Crysis 3, Overwatch, the recent CODs, and Witcher 3. Overall, I'm looking for an ultra quiet-gaming experience.

This is the first time I will be using this particular PC for gaming so all help would be appreciated! Thanks everyone for taking the time to read.

Ambient room temp: 25.5 degrees C
Current specs:
CM HAF XB Cube case
Intel i5-4690k
Asus z97a mb
asus gtx 780
4 sticks of Kingston hyperX ddr3 ram
700w psu
The i5 is running at stock right now with a cheap, generic cooler (same cooling power as intel stock but more quiet).

 

[Mr_Venbeer]

The be quiet! Dark Base Pro 900 is a pretty good quiet case, and doesn't sacrifice cooling. http://www.newegg.com/Product/Product.aspx?Item=9SIA68V45G2217 It's $250 though, but it has so many cool features like a QI charging and is completely modular. You should be able to fit any size cooler (air or liquid) in this case.

You should also check out their Dark Rock 3 / Pro CPU coolers. They are excellent and silent according to most reviews:
http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&DEPA=0&Order=BESTMATCH&Description=cpu+cooler+be+quiet%21&N=-1&isNodeId=1

However, for 4.4 Ghz overclock I would consider a liquid cooler.

 

[Scottray]

A full ATX, quiet, cube shaped case is a tough requirement. Generally, cube shape is mATX or itx. If you don't mind going with a mid-tower, the Cooler Master Silencio series or the Corsair Carbide Silent series may meet your needs.

 

[QuebecActual]

A full ATX, quiet, cube shaped case is a tough requirement. Generally, cube shape is mATX or itx. If you don't mind going with a mid-tower, the Cooler Master Silencio series or the Corsair Carbide Silent series may meet your needs.

I did have a hard time finding a case that fit that criteria too, so I'm open to buying an mATX mobo if there really isn't a full ATX, sound-dampened cube case. I apologize for not mentioning this, but the area where the PC will be moved to has a height clearance of about a foot or 300mm so I wouldn't be able to fit my current CM case either. These suggestions are great though, I'm sure someone will find that information useful.

I'm more concerned on finding a near silent CPU cooler right now though, as I can just add soundproofing material to any case later. Has anyone had experience with the Noctua NH-U14S? How are the acoustics?
I am also looking at closed loop liquid coolers right now, I hope someone can chime in on their acoustics as well.

 

[Mr_Venbeer]

Oh I missed the cube case part. Like Scottray said, a quiet cube case is not easy to find. And considering you want to overclock to 4.4 Ghz, it makes it even harder to achieve a silent gaming PC.
I would personally recommend the Corsair Air 540 case, it has everything you would need. https://www.amazon.com/Corsair-Carbide-High-Airflow-Cube/dp/B00D6GINF4/ref=sr_1_1?ie=UTF8&qid=1482715329&sr=8-1&keywords=corsair+air+540
Slap on some high quality quiet fans like the SP120's and run them on low RPM. That's the option that I would suggest. https://www.amazon.com/Corsair-SP120-Quiet-Twin-Pack/dp/B007RESFR2/ref=sr_1_1?ie=UTF8&qid=1482715352&sr=8-1&keywords=corsair+quiet+fans

For the CPU cooler, choose whichever one you want. Whether it's air or liquid. Then you can just replace the fan with a much quieter one like a SP120 or a Noctua fan. A Corsair H110 would go great with a pair of AF140's:
https://www.amazon.com/Corsair-Hydro-Performance-Liquid-Cooler/dp/B00B4OCW7K/ref=sr_1_1?ie=UTF8&qid=1482715603&sr=8-1&keywords=corsair+h110
https://www.amazon.com/Corsair-Air-AF140-Quiet-Single/dp/B007RESGGC/ref=sr_1_4?s=pc&ie=UTF8&qid=1482715988&sr=1-4&keywords=corsair+sp140
This cooler should Easily push the 4690k to 4.4 Ghz, but it depends on the chip itself if it can go that far.

Noctua NH-U14S is also a decent choice. But won't be as good for overclocking as a higher-end liquid cooler.
Like I mentioned before, the BeQuiet! Dark Rock Pro 3 is a very quiet cooler and performs better than some liquid coolers. Only problem you need to worry about is the installation process as most reviewers have complained about it.