Actually, it does have one and it can be removed/replaced, however it isn't always so easy to do.
Are you sure the device is charged/charging? I would suggest trying to use a different power cord to test on it. First, press and hold the "Power" button for about 20-25 seconds. Then plug it in to the charger and see if it shows as charging. If it does, great. Make sure you do not try and turn it on until it has charged for at least a couple hours. Then try turning it on again.