What cables? Are we talking internal cables, or cables from the back of the tower? Which specific cable does this? Does it shut down, and then reboot to windows? Or does it power down and have to be manually turned back on. Everything point toward psu by what I am hearing but I'm having a difficult time understanding what you are saying exactly. Have you ever used RST? You may want to try this just to weed out a memory problem. Basically you download it and use winimage to make a bootable PC-Dos disk. Run RST and check the memory.
I will upload it to my server, and if any of you would like to download it you can, just make sure you get it in the next few days because I'll delete it.