It sounds like your computer went into sleep mode. Which means when you get it going correctly again, you will need to check the sleep settings and make sure you set it to not go to sleep as quickly.
Many laptops don't seem to want to turn off/on after being asleep. Also, it isn't the power key you usually need to use to turn it back on, but a desktop key. Have you tried that?
If it won't turn off at all, by using the power button, then you may need to pull the battery and leave it out for a few minutes, then put it back in and turn it on. Then go into "Control Panel" and "Power Options". Click on the "Change plan settings" link next to the power option you are using and then on the next screen click on "Change advanced power...