Like all electronic devices, the Blackberry Playbook is prone to issues if its batteries are allowed to fully drain. When this happens the device will neither power-up nor retain a charge when plugged into a power source. The reason for this is due to the way power is managed by the Playbook - batteries need to have a residual amount of power, about 3 volts, for proper power management, below this point there isn't enough to power the CPU and power management chip that regulates the batteries and their power usage/charging. When pressing the power button if the LED flashes red a number of times and then either green or amber, all is not lost.
Note: this is not the same issue as the 'Playbook Black Screen of Death
Depending upon the severity of the battery drain simply plugging the device into the charging unit (not the USB connector but the wall plug and cable unit) should fix the problem - when connected the screen will display a 'power' symbol indicating it's accepting the charge. Allow a reasonable amount of time to pass, at least 30 to 40 minutes, attempting to boot the device. If this does not happen then the following may need to be done.
In instances where nothing at all appears to be happening (aside from a hopefully flashing LED) it may mean the Playbook needs to be 'stack charged
'. This involves charging the device a number of times for a limited period, usually from 30 seconds to between one or two minutes - duration depends on the severity of the battery power loss. Each charge 'stacks' on top of the previous and over a duration builds up sufficient change in the device for it to either boot, or at least then accept a proper charge. In essence, this process builds enough charge for the CPU and power management chip to activate, which in turn allows the device to charge properly. Again, allow a good 30 minutes or so before turning on the device.
If both the above fail then it means the device has absolutely no power at all (not even the LED flashes). In such instances the device may need to be dismantled and the batteries accessed directly for charging - which bypasses the power management system. Needless to say this will void any warranties.