Do you know for sure that the original charger is working? Can you borrow one from a friend and try it?
You can also charge the Kindle Fire from a micro-USB connector that is plugged into a USB port on your regular computer. (The Kindle doesn't charge as fast from your PC, though - the USB port on a PC will only supply 500 mA for that purpose.)
I don't recall such a cord (USB to micro-USB) coming in the box with my Kindle Fire. I picked a cord up somewhere locally - probably at Fry's - and use it to both charge the little beastie and transfer files (music, books, videos, documents) onto it.
Best of luck - I wasn't overwhelmed with my KF to start with, but now that I've loaded some useful things onto it (flashlight, wi-fi analyzer, graphing calculator, etc.), I find myself carrying it around to my various workplaces to use as much more than just an e-reader.