When you connect the Galileo board, the ON LED is supposed to stay always on, not blinking. Also, when you connect the micro USB to the USB port in your computer, the USB LED should remain ON, not OFF. When the board is connected to the computer via USB or serial you should be able to see the Galileo in the Device Manager under the ports tab. I suggest you to try and connect the board via serial cable to your computer and access the Linux side of the Galileo, if the board is not able to boot then the problem is probably the charger. Regarding the charger, the output voltage and current should work, but maybe it is a problem with the cable? Also, which is the firmware version you have?