Try the following and see if it will turn on.
1. Remove the battery.
2. Press and hold the "Power" button for 20 seconds.
3. Now put the battery back in.
4. Plug it in to charge and allow it to fully charge before turning it on.
If this doesn't help, then check the battery to see if it needs replacing.
NOTE: Yes, I know some phone batteries are not so easy to get to, on some devices. In such a case, make sure that your phone is not under warranty still before you try opening it up yourself. If it is under warranty, then contact the manufacturer first.