Beyond the restore suggested by Demo have you tried to give it a reset? Hold down the sleep and home keys for about 20 seconds. If you see the silver apple it's rebooting.
The only other way to look for signs of life - to find out if the whole device is malfunctioning or just the screen, is to hook it up to a computer. Does the computer see it and interact with it or is there no response?
I had my ipad 2 inexplicably go 'dark' on me once. THe screen would not turn on, but then when I hooked it up to the computer the laptop saw it and synced. Then I tried a reset and it came back. So it may be a glitch, or it may be something bigger, such as hardware malfunction.
If the computer doesn't see it and if you can't reset it back then it may be time to take it to the apple store and see what they recommend.