Can you get to the recovery? I haven't tweaked with my moto x much but you can do backups from there. It should show if it actually is charging on the fastboot screen to (I think, don't quote me...).
Most of the options from fast boot end up hitting the white "empty battery" screen for a moment then going screen-off/blinking-green-led for about a minute before flashing the white battery graphic again.
Fast boot says "battery low", nothing about charging and the charger isn't getting warm.
Can you get to the recovery? I haven't tweaked with my moto x much but you can do backups from there. It should show if it actually is charging on the fastboot screen to (I think, don't quote me...).