PC shut down without apparent reason

Here is my pc:
Gigabyte GA-G31M-ES2L (rev 2.0)
Intel E3300
2gb ram ddr2 800 (kingston)
Psu unknown brand (pds) 500w
Windows xp

I've tried to upgrade this PC to win7 x64 with 2x2gb patriot ddr2 1066 memory (patriot pdc24g8500elkr2). It worked fine until pc started to turn off during normal work (browsing etc). No error or bsod appear. I tried to set up timings in bios, according to new ram , also i've raised ram frequency to 1066 and cpu to 12,5x266mhz without success.

Because after that pc refused to turn on, i brought back old 2gb stick and reseted cmos but problem is still happenning.
Is this PSU fault?

After accidental turning off I am not able to turn on pc for a minute or two. Pressing on power button during that minute does nothing (like it is not connected to ac).

Checked temperatures with speedfan, core 0 and 1 around 40, winfast 210 gpu also around 40 degrees centigrade (41,42 sometimes)

Yes, it can be the power supply. Do you have another to replace and test?

Thanks for reply, I'll give it a try.

But, I'm not quite sure if my MoBo supports this RAM memory?

For now, you should set BIOS without overclocking.
Remember that if you rise up the base clock, everything runs faster (CPU, Memory, Chipset etc).
And to get stability, you have to rise voltages up. And it's death sentence.