Problems with powering the Z1 are typically related to the power adapter or the battery not being seated properly.
Power Adapter
If you are attempting to power the device with the power adapter try this. Fully remove the power adapter and inspect both the adapter and the plug hole for obstructions. If no obstructions are found firmly re-insert the plug into the Z1 using a twisting motion.
PowerShell™ Battery Power
If you are attempting to power the device using the PowerShell’s battery, fully remove the battery module and inspect both the battery module and the contacts inside of the PowerShell™ for obstructions.