I couldn't get me 2nd Gen Moto G to charge on either the original wall charger or a USB cable plugged into my computer.  Tried the 2-min Volume Down/Power Off with not results.  Finally noticed that if I held the USB side of the wall charger down just so it started charging.  It must get flattened out with use.  So I placed the wide part of the USB between a pair of pliers and gently gave the pliers a squeeze.  Now it charges all the time.  Note that you should look at the face of the USB when you squeeze it.  You'll see it opening up/turning more barrel shaped.  Don't overdo it—a little squeeze will fix it.

Try using a different set of charger. If still won't work, take your phone to a service center, you may need repair on the charging port.