I would suggest you press the "Power" button for about 25-30 seconds and then plug it in. If it charges great! If not, then you need to try a few other things as it may be the cord, the battery, or the device could just be toast.
First, the cord. Try testing it on another device that can use the same cord. If the cord allows the device to charge, then the cord is good. However if it doesn't, then the cord may well be your problem and you should replace it.
Second, the battery. If you find the cord works fine, but your device still won't charge, then I would suggest replacing the battery. They do wear out after a while.
NOTE: If the device doesn't open easily, as some phones do not, I would not try opening it yourself if your phone is still under warranty.
If your device is still under warranty, you should contact your service provider or the manufacturer to see if they will repair and/or replace the phone.