I guess it's not turning on because the battery is flat because it's not charging.
The most likely reason it's not charging is a problem with the charger - or the USB cable if the charger uses one. Chargers aren't too reliable - the one that came with my HTC lasted a grand total of around 4 charges.
Try a different charger. They're quite cheap on ebay - just make sure you get one that provides the same amps as the one the phone came with.
If that's not the issue then I'm afraid you need to send the phone for repair - hopefully, it's still under warranty.