This message was posted on behalf of Intel Corporation
Thanks for your interest in the Intel Galileo Gen 2 Platform.
I'm sorry to hear that your board is not powering on.
Now regarding your issue, if you look at the image attach below, you will see that in order to determine which component you damage, I follow the line of connection between the damaged component and the nearest IC (TPS652510). Then I examine the schematic of the board and notice that your component is an inductor, see pin 14 (LX1_1).
It is up to you if you want to replace this inductor or if you want to purchase another board.
I hope you find this information useful, have a nice day!