Hardware problems??!?!

Hi guys, I have no clue about computers but there is a problem with it and it is driving me nuts.

I have a toshiba windows 7 intel core i3 laptop. So basically whenever I leave the computer unattended it turns black for most computers right? Well basically I can't turn it back on after. You can see the light for the power still on, but the screen won't light. I tried to press the power button like 10 times and it still won't work. So i had to hold the power button to shut it off and turn it back on. And when it time to shut off my computer, you can see that the power is still on, and you can tell because the system is still running, i can hear it working. I don't know what to do, it is like the 10th time I have to hold the power button button to turn it off and turn it back on. I'm so scared this will damage my laptop. So is there any way i can fix this? or is this a hardware problem?
At first I thought it was a screen saver problem or some hibernating problem but it doesn't really seem to relate with the problem i have now.
PLS GET BACK TO ME ASAP

STUPID question.......how do you go to power setting?

I found the power setting. But what exactly needs to be changed. All i see is
When I press the power button: on battery (sleep) and Plugged in (sleep)
When I close the lid: On battery (Sleep) and Plugged in (sleep)

Is the setting here wrong that making my computer act like that? What exactly needs to be diffferent please help!

Thanks for the help and sorry for the bother but what about the issue with turning off my computer? It is still happening. Whenever i turn it off it isn't totally turned off because I can still hear the system running inside the laptop. Is that a power setting problem that i can change too? if so where do i do that?

I don't know if I am explaining this properly. I tried what you told me and yeah the computer does turn off. Like there is the process of shutting down and when the screen turns black.. The power symbol thingy is still on (lights on). So basically the screen is off but the computer is still running EVEN when i shut it down. I had to unplug the charger for it to turn off or hold the power button to fully turn it off which im scared might damage my computer. I tried the power setting and everything and it still doesn't work so does that mean there is something wrong with my hardware?