Before doing any of the suggested simply try holding down the power button and the home button for 8 seconds. This will restart the device.
If that doesn't work then try charging it as suggested, using a different cable. Have you had any charging problems previously?
If that fails trying placing the phone into its recovery mode, we will need iTunes on a computer for this. Plug it into the computer and hold both the power button and home button for 8 seconds, after this let go of the power button but keep holding the home button. We should get a message on iTunes.
If this fails then the phone will need a service.