6-pin PSI-E for GPU only half connected to power supply?

The Song

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Sep 7, 2013
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So I installed a new video card yesterday, and unlike my old one it requires extra power via a 6-pin PSI-E. It did come with a cord for that of course. That said, here is my confusion: The one side of the cord is the 6-pin, and thats all fine and dandy. The 6 parts of the 6 pin, however, are split into 2 of the things that you would connect to the power supply, but my computer only had a place to plug in one of them (meaning I've effectively connected 3 out of 6 of the pins, or so that was my original thought). Having nowhere to plug the other one in, I figured I'd just try it out this way, and it did work. I turned my computer on and installed all the software for the new GPU all seemed well. After that I figured the other one of the 2 plug-ins from the 6-pin was for if I had to connect something else to the power supply, making a chain from component-to-component-to-PSU or something. Now I am uncertain, because my computer has turned itself off (instantly) while I was playing LoL and The Darkness 2. I know my build surpasses the requirements of those games. So here is my main question: Does the cord for my GPU's 6-pin have 2 plugs so I can connect something else, or do I need to find a way to connect both directly to the Power Supply. (Hopefully there are adapters to give you more plugs to work with?) If it is for making a chain, then I need to know why my computer is crashing. I do believe it is overheating, as nothing else seems possible after checking logs and whatnot. Could my new (larger) GPU be blocking the heat escape from some other part or something, maybe?

My Specs, because someone would probably ask for them:
CPU: AMD FX-6300
GPU: Nvidia GeForce GTX 750 Ti
Ram:8 Gigs
OS: Windows 8.1

Edit/addition
PSU: HMW 600 Watt ATX Power Supply Model: XG-H600.

the 750 Ti is the new one, the old one was just a GeForce GT 640

Umm,......I don't know why I kept saying PSI instead of PCI
 

The Song

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Sep 7, 2013
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good thought I somehow didn't have. Updated original post.
 

The Song

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Sep 7, 2013
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Updated original again. When I opened my computer the PSU had only one thing to plug stuff into left, whereas my new GPU came with a cord with 2 plug-ins. (It was the correct plug-in; PSI-E.) My old video card didn't need extra power.

........I don't know why I keep saying PSI instead of PCI
 

The Song

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Sep 7, 2013
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Unfortuneatly I don't have access to a camera, but I found a picture matching the cord came with online.
molex_pci-e.jpg

My computer only had a place for me to plug in one of the white end-pieces, the black piece of course connects to the GPU
 

The Song

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Sep 7, 2013
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I can't even find my power supply online, but anyhow do you see the picture I put in my reply to Kian? Well, my PSU has one of what you would plug the white end-pieces into. There were of course lots of other cords that I followed, all of which were plugged into other hardware (Motherboard, hard-drive, fans, etc.) So yea my PSU has one pcie port-thing, I need to know if I need to turn it into 2 or if my issue is unrelated.
 
you dont need to use this adapter of yours. since you have a pcie port thing as you say, connect it directly to the gpu. that adapter is meant for use with psu that doesnt provide a pcie cable, a connection though which isnt recommended!also since we cannot track your psu we cannot determine(estimate) its quality.anyway since it actually provides a pcie cable, it should suffice!
 

The Song

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Sep 7, 2013
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.....................*sighs at own failure........................

So I bought a can of compressed air while running some errands, and while spraying out dust I noticed this rather subtle piece of plastic still on my GPU. Took that off, haven't had a problem since. Figures, doesn't it?