The Quil does not hold a wireless charge and can't be powered through a computer's USB port.
The first thing that you need to check if your pen is not powering on is whether or not the AC adapter is plugged into the wall socket correctly. If so, you should confirm that the USB port is inserted correctly into the AC adapter. If, you still have no power you will want to confirm that the power plug is securely inserted into your Quil’s power port.
If you've checked all of that, try plugging the Quil into an outlet that you know is working, if it still doesn't power on please contact customer support.