I want to make sure that your issue is well resolved. As there are different versions of the DROID line-up, can you please verify the exact model?
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If you have a Moto Droid Z/Z Force:
These are examples of the charger not fully inserted (device may show empty charge icon but still not charge device.)
Picture 1: https://motorola-global-portal.custhelp.com/euf/assets/images/faqs/Mods/z-battery-1.png
Picture 2: https://motorola-global-portal.custhelp.com/euf/assets/images/faqs/Mods/z-turbo-1.png
These are examples of a fully inserted charger (device shows charge icon with TurboPower Charge % and charges properly)
Picture 1: https://motorola-global-portal.custhelp.com/euf/assets/images/faqs/Mods/z-battery-2.png
Picture 2: https://motorola-global-portal.custhelp.com/euf/assets/images/faqs/Mods/z-turbo-2.png