PC shutdown, failing to even power back up!

[Validations]

***Warning: long story before question***

Several days ago while gaming on my PC, it randomly shutdown and wouldn't turn back on. I waited a few hours, still wouldn't turn back on. So I decided to try to diagnose the hardware issue.

First I checked if the PSU was still good. I removed it from the system and plugged it in alone to the wall, pressed the button on it, fans worked, light lit up. Seems okay, so I plug it back into the system. Press the switch again, and all I get is a short noise as if it's going to startup, a fan movement for a split second; all before it just stops and goes dead again.

I assumed it wasn't the PSU, so I then unplugged the GPU and the optical drive and tried again. Surprisingly, it actually worked. All system fans came on, lights, etc. Even the light on my GPU came on, even though I unplugged the two 8 pin connectors...maybe the MB gets it power? Which would make me think the GPU isn't the cause of the problem.

After plugging in the optical drive and the GPU, it didn't work. As it turns out, the system powers up so long as I don't plug anything into the left 8 pin connector. If I plug either connector in the right alone, it's fine. So the question is...

Is something wrong with the GPU or PSU?

----- Tech Specs: -----
Central Processing Unit:
2nd Generation Intel Core i7-3820

Operating System:
Windows 7 Home Premium, 64Bit, English

Random Access Memory:
16GB Q DDR3 SDRAM at 1600MHz

Hard Disk Drive:
1TB 7200RPM Storage

Graphics Processing Unit:
NVIDIA GeForce GTX 690 4GB GDDR5

Optical Drive:
Single Drive: 24X CD/DVD burner (DVD+/-RW) w/double layer write capability

Power Supply Unit:
DELL Precision T5500 875W POWER SUPPLY N875EF-00 NPS-875BB W299G

 

[C12Friedman]

I would lay odds on the PSU being the problem here, the 690 takes a lot of amperage on the 12v rail(s), likely the Dell PSU isn't up to snuff

 

[xbread]

I agree with C12Friedman on this one. Dell PSUs aren't the best quality, and it probably doesn't have the juice to power the 690 (or the rest of your components really). If you can borrow a working, high quality psu from someone (from brands like Corsair, Seasonic, etc.), then you can see if the culprit was either the gpu or psu.