Have you checked to make sure it is fully charged? Try holding down the "Power" button for 20-30 seconds and then plug it in to charge. If it shows the battery charging, great. If it doesn't, then it could be the cord or the battery that are not working.
Next I would try another cord. If that doesn't work, try a new battery. If in the end, none of that works, your only other options are to contact the manufacturer or your service provider (if it is still under warranty) and see if they can repair or replace it. Should none of that work (including contacting the companies) then you may well need a new phone.