First I would check the battery, it could just be very dead and need a longer than usual charging.
Should that not be the case, then you should open up the phone and check to see if there is anything in the space with the battery, that could be keeping it from correctly connecting to the phone. Also check that the battery isn't bloated at all. If it is bloated, you definitely need to replace it.
You can also check to make sure your power button isn't stuck. Check it for lint or dust.
If none of this works, and you have a USB cable for the phone and a windows computer, you can check the phone to see if it is having any problems. To check it do the following.
1. Plug the phone, via USB into the computer. When it asks you how you want...