No boot but keyboard lights up

[lemmoncake]

my new computer which i had for about 1 month psu died so i got a replacement sent. i installed it to find that now the new one worked for about 3 mins all fans turned on sounded all fine but was having problems with my monitor getting signal as i was playing with the cables at the back of the monitor and my whole computer turns off...
i leave it a few mins and turn it back on and fan lights come on for a spilt second then stop and the keyboard lights stay on.
i hold down the power button for about 30 seconds then the keyboard turns off if i press the power button again flash of light no start up and keyboard is on again!

if you have any ideas please let me know!

this is my build:

Mobo:
ASRock Z77 Extreme 4, Intel Z77, S 1155, DDR3, SATA III - 6Gb/s, SATA RAID, PCIe 3.0 (x16), D-Sub/ DVI-D/ HDMI, ATX

Cooling:
Cooler Master Hyper 212 EVO, 4 Heat Pipes Direct Contact, with 120mm Quiet Fan LGA775/1155/1156/1366/AM2/AM2+/AM3/FM1

Graphics card:
3GB XFX Radeon HD 7950 Double D, Black, Ghost/HCell, 5500MHz GDDR5, 900MHz, 1792 Cores, HDMI/mini DP+

Screen:
Acer S230HLBbd DVI LED Full HD DVI/VGA 1920x1080 250cd/m2 100M:1 5ms Black

RAM:
8GB (2x4GB) Corsair DDR3 Vengeance Low Profile Cerulean Blue, PC3-12800 (1600), CAS 9-9-9-24, XMP, 1.5V

DVD Drive:
Samsung SH-118AB/BEBE Black 18x SATA DVD ROM - OEM

PSU:
550W xfx pro

OS:
Microsoft Windows 7 Home Premium 64 Bit SP1, Operating System, Single, - OEM

Hard drive:
3TB Seagate ST3000DM001 Barracuda 7200.14 SATA III 6GB/s 7200rpm 64MB Cache 8ms NCQ OEM

CPU:
Intel 3rd Generation Core i5-3570K CPU (4 x 3.40GHz, Ivy Bridge, Socket 1155, 6Mb L3 Cache, Intel Turbo Boost Technology 2.0)

Case:
Coolermaster Storm Enforcer Mid Tower ATX Case

 

[TheProudNoob]

Try basic troubleshooting.

Have you checked if the monitor is broken? Maybe the outputs on your GPU or the inputs on the monitor? The cable?

Is your GPU seated correctly?

Your power supply also seems a bit weak for a high end GPU. If you can, test your PSU in another computer, and see if it works. If you can't, try switching your graphics card for a less power hungry one or if there is a switch for performance vs quietness, turn that to quiet.