Computer not powering up

[OptimusGrime10]

Hello all!

First off I would like to thank you all in advance for your help with this matter as this is the first computer that I have modified.

I bought this computer:

Technical Specifications:

Operation System
Genuine Windows® 7 Home Premium 64 bit
CPU
AMD Phenom II X6 1045T 6-Core 2.7GHz
Memory
8GB DDR3 1333MHz
Graphics
ASUS EAH5450 1GB DDR3 by ATI Technologies
Hard Drive
SATA 1TB 7200RPM
Optical Drive
16x DVD+/- RW Dual Layer Burner
Expansion Slots
(2) PCI
(1) PCI-e 16x (occupied)
(1) PCI-e 1x
(6) SATA (2 occupied)
(2) 5.25” Optical Drive Bays (1 occupied)
(3) 3.5” Hard Drive Bays (1 occupied)
LAN Interface
10/100/1000
Audio Interface
ALC887 High Definition Audio 8-Channel CODEC Channel 8 S/PIDF out
Front Panel
16n1 Card Reader (SD/microSD/miniSD , MMC/microMMC/RS-MMC, MS Pro/Duo/Pro Duo, CF)
(1) Headphone Jack
(1) Microphone Jack
(4) USB 2.0
Rear Panel
8-Channel (7.1) HD Audio
(1) RJ45 LAN
(1) VGA
(1) DVI-D
(1) HDMI
(1) S/PDIF-out (Optical)
(6) USB 2.0
(1) PS2
Power Supply
400W (PFC) Peak
Dimensions
8”W x 18”H x 19.5”D
Weight
26.4 pounds

Which I got from Woot here: http://www.woot.com/blog/viewentry.aspx?id=17217

I upgraded the Graphics card to this:

Sapphire Radeon HD 5770 1 GB DDR5 2DVI/HDMI/DisplayPort PCI-Express Video Card

Seen here at Amazon: http://www.amazon.com/gp/product/B0035K6H2C

I then upgraded the Power supply to this:
Corsair CMPSU-430CX CX Series 430-watt Power Supply Compatible with Intel Core I7 and Core I5

Seen here at Amazon: http://www.amazon.com/gp/product/B003YBVN08

I installed everything and it was working fine for awhile until one day the power shut off.  I attempted to restart the computer but it would only power on for about one second then turn off.  I thought that perhaps it was the power supply so I switched out the new power supply for the old power supply.  The same issue occurred; the computer will power on but only for a couple of seconds then turn off.

I do not know where to go from here. I am hoping that it is a simple fix and that I can replace one or more components. 

Thanks again for your help in advance.

[OptimusGrime10]

Oh and to help clarify there are no beeps when the computer starts and no noises other than the fans on the power supply and video card starting then stopping.

[Lumpy44]

Had this issue once before too. Had a short in my power supply. Replaced the power supply and it booted again and ran for about a minute and did the same thing. Found out that it shorted out my mobo too. Had to replace both. Hope this isn't your issue, but worth a look.