Like Eddy said, EVEREST is great program for checking up your system. Try using it and see what it reports. Best of all, it's free.
Power management - go to Desktop, right click it, choose Properties, and then go to Screensaver tab. At the bottom of that window click on Power... button. You should see what power scheme is enabled at your system. If you click on Hibernate tab, you'll see is it enabled or disabled. I keep it always disabled.
However, no matter how your power scheme is set, that couldn't be the problem for not being able to start your computer. As I said, over 80% of all causes is bad power supply, bad memory or even defective motherboard.