Need help identifying PSU problem / replacement

Hellow!

Yesterday I posted a thread on graphic card compatibility, I found out that my PSU does not support the card I choosen, I was recommended with a Radeon HD 7750 that seem to use only about 250w (I have 270)

However, I have one problem with this computer that I fear it might effect the card's performance and other danger.

My computer was once got shut off abruptly by a power outage, it was plugged into a surge protector, but the computer would't turn on after.
I opened guy and could't find anything wrong, but pressing the power button doesn't do anything.
I tried unplugging the cord and replug and it doesn't work either. Until I unplugged the power supply from the MOBO and plug it back in, the power light flashed (blue light) and the fan ran for a second, then stop, and I have to repeat this until I able to turn it back on by pressing the power button, it's EXACTLY like starting up a OLD CAR! You know in those movie when the car would'r start and go mgrrrr mgrrr mgrrr, then if you tried enough it would start, it EXACTLY what my computer is like now.

It very random, most of the restart and shut down would work fine, but if it got turn off abruptly then I'll have to open the guy and "kick start" it.
I'm not sure, but I'm guessing this a PSU problem?

If it so, can you all recommend for me a PSU in $50 budget that can handle card like :
http://www.amd.com/us/products/desktop/graphics/amd-rad...

Oh and here's the inside if you want to take a look
http://imgur.com/a/h5sDW#5
*spec*
My PC specs:
AMD Phenom(tm) 9550 Quad-Core Processor
2.2 GHz
Microsoft Windows Vista Home Premium Edition Service Pack 2 (build 6002), 64-bit
6.00 GB RAM
*spec*
Thank you for your help!!!!