There are 4 reasons why your unit is behaving this way:
1. Charger is the problem.
2. The docking station is the broken.
3. The battery is broken or not accepting charge.
4. The actual unit is the problem.
It is very hard to tell which one is causing this to happen.
Let us do some troubleshooting first:
1. Plug your charger in an A/C outlet and make sure the red power light (left) is lit, otherwise the charger or the docking station is broken.
2. You can test the charger with a multimeter. Unplug the charger from the docking station and measure the voltage across the outside and inside, it should register more than 5 volts DC. If there is a 5Volt DC the docking station is the problem otherwise the charger is broken.
3. If the red power light is lit and the status light (right) is lit too, your docking station is broken.
4. If the red power light is lit, dock the unit into the charger, the status light (left) should turn red when your battery is accepting charge or turn blue when your battery is fully charged.
5. If the status light will not lit at all (while the red power light is on), tap the screen while the unit is docked on the charger. If the unit will become alive, you need a new battery otherwise you need a new unit.

12 hours is very long time to charge, the status light should turn to blue in less than 2 hours especially for a new battery.