Is it connected to a surge protector? This will happen if it gets a power surge and powers on. I've seen this many times on PS3s as well.

Are you getting indicator lights? Does it charge? Any signs of life when you press the power button? If you get nothing at all, it's a good idea to discharge the power circuit. Remove the battery and AC cord. Hold down the power button for 10-30 seconds. Without letting go, reattach the AC cord and continue holding power for another 10-30 seconds. Release the button and try turning it on normally. (On Windows machines, this is also a good way to clear the CMOS on some machines.)

I've found Batteries Plus to be a good source for laptop and mobile batteries. Most are brand names like Duracell. They do sell batteries for Apple devices. Looks like the iPhone batteries are Rayovac.

Does it have a red kickstand? It's most likely a HTC Evo 4G LTE from Sprint.