Your power adapter/charger may be faulty. Try this method and see if your Nabi starts to charge.
Pull out the cable from the power adapter, plug it into a USB port of your turned on computer, then plug the charging tip into the Nabi tablet. If it starts to charge your adapter is faulty and should be replaced..
If this method doesn't work it could be either that the cable, the charging port in the Nabi or the battery in the Nabi is faulty.
This method will take longer to charge the Nabi than a power adapter. Please allow it to charge for several hours.
You cannot use a standard mini USB to USB cable to charge the Nabi, because it only charges via the Power Charger port and not the mini USB port.