Do you use the Arduino expansion board?
In that case, what was the current external 12V power supply? Because if it is more than 1A probably you brake the supply switch.
I did it yesterday!!
You can try to power the Edison from one of the microUSB ports, the microUSB nearest to normal USB port. Control that the switch between the two ports is properly positioned. The supply via the USB jump the switch that you probably damaged and you can use the edison. It worked in my case!!
Before your board started to fail and you could no longer boot from USB, were you able to access the Linux console and upload the blink example successfully? Also check out section 2.3 of https://communities.intel.com/docs/DOC-23252 and make sure you are using a proper power supply.
The edison breakout board required the external power supply between 7~17V.
I installed the edison to my robot, my robot battery power is 16V. (12V in the title is wrong, sorry for this)
I realized that when my robot is in charging, the battery power may come to 18V.. Don't know whether this is the root cause.
But do you know why it will break edison core module? I think there should have some protection in core module.
If this is the case, any method to repair the core module?
The external power supply for the Arduino expansion board is different than that of the breakout board. According to https://communities.intel.com/docs/DOC-23252 , the power supply for the breakout board is between 7V to 15V, so an input of 18V is likely to damage your board.
I've seen 12V DC power adapters generate 18V when unloaded. And 18V from those same power supplies was enough to fry the first set of DC-DC convertor switches. I now have a sample set of 1 instance; so I now warn people that unloaded power supplies could start at damaging voltages. If your battery charger raised the voltage above 17V, then it's likely the charging circuit blew the Edison's DC-DC convertor.
For everyone else: Edison-Arduino breakout boards are damaged when 18VDC is applied to the power connector. Always check your power supply's unloaded voltage with a voltmeter before your first attempt to power on the Edison. Even DC power adaptors with a 12VDC on the label might actually generate 18V when first connected to an Edison.