Maybe you should try and remove the back off it, where the battery is, then take out the battery, dust it a bit then put it back in. 

Try and turn back on your phone.

If not, go see a phone technician, the battery could be damaged/broken, but where did you buy the phone? If it was offline (Ebay, Amazon etc.) I would see the phone store its running with. (Like Tesco Mobile, EE, Three, Orange, Virgin etc.)