Failure to Boot, No Display, Computer Turns off and on (PSU or Mobo failure?)

[13illay]

SPECS:
EVGA 780 Ti
Intel Core i7-4770k 3.5ghz quad-core
ASRock Z87 Pro3 LGA 1150
Corsair Vengeance 8 GB (2x4) DDR3
Rosewill Stallion Series 700w PSU
Windows 7

So, my computer has been working fine up until this morning. I built it around half a year ago. When I turned it on this morning, there was no display with no beeps. When I turned on the computer, it turned off after about 5 seconds. So I used the other RAM stick. Same results. Then I reset the CMOS and tried both sticks separately again with the same results. I put both back in and now it will not stay on for more than 5 seconds and continues turning on and off.

Next, I tried taking out EVERYTHING except the CPU and Mobo. The computer stayed on, but still no display from the on-board graphics. I put the 780 back in and it still stayed on. Then I put the RAM in and it would turn off. Unfortunately I do not have any spare RAM lying around to test if it's the RAM itself. What is strange to me, though is that this started out of the blue, which leads me to believe one of my parts has stopped working.

I'm not too great with computers, but I'm guessing it's either the motherboard, the RAM, or the PSU, but I really don't want to spend money on either of these parts only to figure out I was wrong afterwards. I could use some advice. Thanks.

IN SHORT: My computer only stays on if it has the RAM removed, but even with the RAM installed, there is no display from either the on-board graphics or the 780 Ti.

[B]Solved it:[/B] Keyboard controller/Gate A20 failure. Motherboard issue.

[lavacano]

I seem to remember that Rosewill PSUs were extremely bad juju

[gbtygfvyg]

Rosewill are shit PSUs. Every single one I got was met with a high DoA rate. Stopped bothering after my 2nd one. 3 tries on my first one, another 3 on my second one, all of them DoA. Actually the 2nd try on my 2nd Rosewill PSU worked for a whole 1 hour before it stopped working entirely.

[Levelog]

Some are, some aren't. Some like the Rosewill Capstone are absolutely top notch units made by Superflower. Others are fantastic budget ones. There certainly are models out there that are trash though. Same with every other rebrander.

[13illay]

Turns out it was a motherboard issue. My chassis speaker turned out to be broken after I replaced it with a new one and it gave me six beeps. Which means...
Keyboard controller/Gate A20 failure