Sorry to hear you are having issues with the Moto G.
From the Motorola troubleshooting site: Motorola Support - Find Answers | Motorola Mobility, Inc.
If you are seeing a question mark on the screen this may be a symptom that the battery is not recognized.
Please check the rear housing for any damage or detachment.
Damage or attempted removal of the rear housing could have resulted in the battery no longer being recognized.
The phone will need to reach a minimum charge of 5% before it will power-up.
Please follow the steps below to charge and power-up the device:
Without pressing the power button, plug in the device to the supplied wall charger and into an electrical outlet (not a USB port).
Within 30 seconds your device should display a battery meter indicator. If the battery meter is red and below 5% the device will not power up.
If you do not see the battery meter after 30 seconds, please press and hold the Power button for 10 to 20 seconds with the device plugged in, the device will restart and go through the normal boot-up sequence.
Once the display lights up you can let go and monitor the battery meter. The battery meter will go away within a minute and you will be required to press the Volume Key periodically to monitor the meter.
- When the battery meter reaches a charge greater then 5% you can power the device on.
Please note: It will take approximately 15-20 minutes with the supplied charger to charge the device to a minimal level to power the device back on. Do not use the charger connected to a USB Port as the charging rate is much lower and could take a few hours to charge the device to a minimal level.