Plug it in
If your phone has notification lights, as most do, this is also a good way to see if the charging indicator comes on. That will at least tell you the circuit from the USB to the main board is intact. If this works, you may just have a bad battery, which is easy to replace. Buy a different battery and cross your fingers. If you get no response here either, it may be time to take more drastic steps.
You can also plug it into a computer to see if it is recognized as a USB device. If so, it is probably running, but the screen just cannot turn on. Proceed to the next step if that's the case.
Text and call to check behind the scenesIf you are not near power (or your results were inconclusive), you can always have someone send a text to your phone. It is not unheard of for a phone's power button to be bad, meaning you cannot wake it up. Unless the phone has other physical buttons that will wake it up (many don’t) it could look dead. Similarly, your screen could have gone bad. The symptoms would be similar at first (although the buttons may light up if just the screen has gone bad).
You can check to see if your phone is running behind the scenes by having a friend or acquaintance send an SMS or call the phone. If you get a notification sound, or the screen comes on for a call, you most likely have a bad power button. This can usually be fixed fairly cheaply if your phone is not under warranty. If it is, head to your carrier and have words, as this is a hardware defect. If the screen doesn't come on for calls, but you get notifications sounds and rings, the screen could be broken. You may want to run through the next step, though. Just to make sure.
Pull the battery
When you drop the battery back in, see if you can get the phone to restart. Note if the screen comes on, and if the system buttons light up. If the phone still does not boot up, take a look at the battery compartment. There will be a small square of what appears to be white paper embedded somewhere in this area. This is the moisture indicator, and if it has turned pink or red on part of its surface, your phone has probably been exposed to water. This means your warranty is shot, and the phone is probably dead. It's really a worst case scenario since you can really only have the phone repaired at your own expense, or sell it for parts.
Use recovery mode to wipe the phone
The screen you get to will be mostly text, but you should see Recovery as an option here. Select that, then you will get a screen with a phone and an exclamation point over it (on most devices). You will need to press a series of buttons here as well, and again this will vary by phone. When Recovery is fully loaded up, you can pick factory reset.
If you still cannot get the phone to boot properly, you're going to have to take the device to your carrier or manufacturer. If it is under warranty, you'll probably get a replacement. If not, you may have to pay for a refurbished or new phone.
If your phone refuses to wake up, just take it easy and follow these steps. If you are a rooter, you can try reinstalling your ROM from recovery if the phone works at all, but most users will be stuck with the stock options. Before you go to your carrier, trying to figure out what the problem is can make things go much more smoothly. Having the full story is usually easier than just handing them a broken phone and waiting for them to figure it out. If you have any tips for troubleshooting a seemingly dead Android phone, let us know.
Image Credit: XDA