Chosen Solution
My 16g 1st generation iPhone won’t charge. I have tried the USB port on my Imac, the wall charger and my car charger as well as chargers at the local apple store. Since it is off warranty, the Genius bar folks were of no help. The battery symbol in the upper right corner never shows the “charging” mode.
I would try replacing the battery, if that doesn’t work it could be you need to replace the logic board.