New Droid 4 doesn't charge, green light goes on then off, do I need charger?

Hello and thanks in advance for any assistance.

I just purchased my first smartphone, a Droid 4 by Motorola, factory refurbished, but I can't turn it on. There's no SIM card (still coming in the mail) and the battery is presumably dead, but when I plug the phone into my computer via the USB it came with then a tiny green light at the top left of the phone appears for about two seconds and then disappears and that two seconds of green light is the only response I've been able to get from the...

New Droid 4 doesn't charge, green light goes on then off, do I need charger?

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