Will all of this fit inside my 16.2"x6.8"x16.7" case?

Solution
GV-N970IXOC-4GD won't even go past the edge of a micro-atx motherboard, so it will probably fit.

Avoiding changing your psu is a bad idea, since overloading it could ruin all the rest of your hardware. EVGA makes psus of varying quality, and I'm not sure how good the one you linked is.

As far as a graphics card on par with the gtx 970, take a look at the gpu hierarchy chart:
http://www.tomshardware.com/reviews/gpu-hierarchy,4388.html
It's a high-end gpu, so it needs a high-quality psu. iirc, the strongest gpu that can run just off the pci-e slot power (not requiring 6-pin or 8-pin connectors) is the gtx 750 ti (quite a bit weaker than a gtx 970), and only certain models work that way.
Those are presumably the exterior dimensions, which are not enough to determine whether those parts will fit. Do you know the manufacturer and model, or can you post some photos of it (especially of the interior, with the side panel off)? At that size, there's a good chance (though maybe not 100%) that it can fit a micro-atx motherboard.

You haven't listed an aftermarket cooler, so I presume you plan to use the stock cooler, which shouldn't need to be checked for fitting in the case.

The video card, however, is somewhat long at 269mm, so I'd need to know what the internal layout of the case is like, including whether it has one or more removable/re-positionable hard drive cage, before I can say whether it will fit.
 

happyt0mat0

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It is my old computer case, and I don't think there is a model for the case. My old computer is this: http://support.hp.com/hr-en/document/c04336643 and I'm only replacing the RAM and Graphics card. I'm really just looking to see if my graphics card can fit inside.
 
Even if it technically fits (which I still can't say for certain without a picture of the interior, or you could grab a tape measure and find out for yourself), I seriously doubt that HP case has suffiicent airflow to support that graphics card (edit: especially if you get a fanless psu, since the psu fan was probably the only thing providing any airflow at all through that case). You'd be much better off buying a new case to handle it.

I see a couple of additional problems, now that you've revealed what you're upgrading from:
1. The psu you chose is 20mm longer than the one that came with your prebuilt computer, so the modular connectors will probably get in the way of the optical drive cables (unless you plan to remove the optical drive)
2. Prebuilt computers come with OEM copies of Windows, so when you replace the motherboard, you'll need to buy a new Windows license if you haven't already (and probably get a new installer for Windows as well, since the install disc that came with the computer probably includes other software and drivers that are specific to the prebuilt)
 

happyt0mat0

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I can definitely remove the optical drive. In my almost 2 years of using this computer, I've never put a CD inside this computer. If I remove it will it solver the problem?
 

happyt0mat0

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Wait... I misunderstood. I'm only changing the RAM and the GPU and nothing else.
 
You mean you intend to run that gtx 970 on your HP Envy's original power supply? I strongly advise against that. Prebuilt computers come with psus that are just enough for the hardware they ship with, not for upgrades, and they're generally low quality.

The psu you chose in your initial pcpartpicker link might seem like the same level to you, since it has the same claimed 460W output, but Seasonic has a good reputation for quality, and that unit supports 38 amps output on the +12V rail (which is where it counts, a gtx 970 system needs 28 amps there (reference link), so even though the normal recommendation is 500W, that psu is probably ok; the HP doesn't list specs on the site for the +12V rail)

Also, the video card you chose has a design that vents the heat into the case instead of out the back, so you need a case with plenty of airflow (e.g. two 120mm intake fans and one 120mm exhaust fan) for that to be safe.
 

happyt0mat0

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Is there another graphics card doesn't require as much wattage, and doesn't vent the head into the case? but equally as powerful as the gtx 970? I doubt my case has strong airflow, but I don't know how to check (help on that). If there's no other way, do you think this PSU is strong enough: https://www.amazon.ca/dp/B00H33SFJU/?tag=xov-can1-20 but I prefer to not need to change my PSU.

(unrelated) do you think this graphics card: GV-N970IXOC-4GD will fix the size issue mentioned before?
 
GV-N970IXOC-4GD won't even go past the edge of a micro-atx motherboard, so it will probably fit.

Avoiding changing your psu is a bad idea, since overloading it could ruin all the rest of your hardware. EVGA makes psus of varying quality, and I'm not sure how good the one you linked is.

As far as a graphics card on par with the gtx 970, take a look at the gpu hierarchy chart:
http://www.tomshardware.com/reviews/gpu-hierarchy,4388.html
It's a high-end gpu, so it needs a high-quality psu. iirc, the strongest gpu that can run just off the pci-e slot power (not requiring 6-pin or 8-pin connectors) is the gtx 750 ti (quite a bit weaker than a gtx 970), and only certain models work that way.
 
Solution

happyt0mat0

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The PSU by EVGA has very good ratings from several sites and positive reviews also. So, if I buy this PSU, I can keep this GTX 970. The other option is not replacing the PSU and getting a weaker GPU. Will I need a new case for a better cooling system of I want to choose the first option? Edit: to clarify, this new PSU does have 2x 6 pins right?
 
I'm not sure where you found "several" sites that reviewed that specific EVGA model (sites that properly test psus are a much better source than user reviews), but based on this review, I'd say it's adequate for a gtx 970. I'd still suggest getting a case with better cooling, but you might be okay for a few months while you save up for that.
 

happyt0mat0

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It "might" be okay for a "few" months... *gulp* what happens after that...?
 
Sorry, I wasn't thinking straight. That Gigabyte gtx 970 still has the problem of venting the heat into the case, which can lead to overheating issues. If you can limit yourself to short gaming sessions (say 30 minutes at a time, with 5-10 minute breaks), you might avoid that. There are also programs like HwInfo you can download to monitor temperatures and figure out how short your gaming sessions really need to be.

Alternatively, I found this: http://pcpartpicker.com/product/62FXsY/evga-video-card-04gp41972kr
It's more expensive than the Gigabyte card you were looking at, unless you're willing to consider a used model, but it uses a design that blows the hot air out the back, and thus is less dependent on case airflow. Also, at 241mm, it's shorter than the 244mm width of a micro-atx motherboard, so it will hopefully fit.
 

happyt0mat0

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With this graphics card, does it require 2x 6pins? If it doesn't I don't think I'like be upgrading my PSU. Correction: that isn't available to me, for I am in Canada.
 

happyt0mat0

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I don't think I can dish out 450$ for a single graphics card ;_;

Will this graphics card work? http://ca.pcpartpicker.com/product/Xp98TW/evga-video-card-04gp42972kr (worried about it's size)
 
It's 241mm, so you should be okay on size (the micro atx board that came with your HP is 244 mm wide), but a dual-fan design like that will be venting most of the heat into the case, rather than out the back, similar to some of the other cards you've considered.

I don't understand why you're being so stubborn about getting a new case. http://ca.pcpartpicker.com/product/C9zv6h/cooler-master-case-rc912kkn1 (which is in stock at the moment at DirectCanada, despite what PCPartPicker says) costs a lot less than a new video card, will last through many years of upgrades, and should be able to handle just about any video card you can find (both in terms of airflow and length).