It is an htc Evo phone which I've had for a few years. I noticed the phone got very hot and then I couldn't start it. I probably recharged it for too long. It loses power very quickly.
I would personally take the phone to a place that can run a diagnostic test on the phone before spending money on a new battery. Here in Ga we have places called "CPR" (cell phone repair) and they generally do not charge to run diagnostics. If there is an issue then they can tell you what it is before you go and waste money on a battery if that's not what the problem is