Solution 1: Battery pull
Do I need to explain this? Open the back cover, remove the battery and leave it for about 30 seconds to one minute. Then put the battery back and try to turn it on. If you take more than 2 minutes to do it, you need more practise :)
Solution 2: Power button FTW
Another reason why your Android might not turn on is because of heavy modding or extreme undervolting. Well, what you can do is to hold the power button for 15 seconds and if the phone reboots itself, then it is good new. If not, you got to try the next solution.
Solution 3: Using power button and wall adapter
This would probably the easiest way to turn on a 'dead' device. Simply just plug the adapter into the wall and hold the power button for the next 15 to 20 seconds. You will see that it will start to boot up (and this is where you start to figure out what is wrong).
Solution 4: Clockwork Recovery a.k.a. CWM Recovery
Okay, whenever your device goes black, try to go into Clockwork Recovery or CWM mode. Clear dalvik and cache first to see if the device is able to boot up successfully. If it fails, then you should either undo what you had done or simply select the latest backup you had done.
Solution 5: Odin, the almighty
If solution 1 and 2 doesn't work at all, then you should just use Odin. For newbies, Odin is a program which equals to either Absinthe or redsn0w on Apple jailbreak process. Download the latest and safest rom and kernel and use Odin to reflash it. With this, you will probably be able to turn on the device as usual again without much hassle.
There are probably 10 or more ways to get your phone booted up but again, these are actually the fastest way to turn on your Android. Hope this works well for you and good luck!