PC turns off a few moments after turning on

Hi, every morning when I turn my PC on it turns itself off after about 5 seconds. Once it's off, pressing the on button does nothing. I have to flick the PSU switch at the back off and on again for the front button to turn the computer on again. It'll then turn itself off again after a few seconds and I have to repeat the process. Eventually it decides to stay on and it boots up fine.

Any ideas what this might be? I'm worried that one day it just won't turn on at all. One thing that might be worth mentioning is that if we've had a powercut in the house at all, even when my computer is switched off, when power resumes and I turn my computer back on, it tells me there's a CMOS checksum error and my BIOS settings are restored to default, as well as the time in Windows being set to 2003. How can this happen when my computer wasn't even on at the time of the powercut? No idea!

Any help would be great, sorry for the long post.

Last night we had a powercut just as I was about to shutdown my computer and go to bed. The morning after I turned my computer on and it came on first time. Weird. When I shut it down the normal way the next time I turn it on it takes about five attempts as described in the first post.