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The black line is not a burnt trace, it is a crack that separated a voltage pin from a voltage plane. The round solder joint to the left of the G in 'GND' is OK. The round solder joint directly below the N in 'GND' has been broken away from a voltage plane, and should NOT be connected to GND. 
Instead, it should be jumpered to one of the two pins above C7. C7 is a cap that decouples across a voltage. If you follow the thick trace around the top of the board, it goes to the opposite side of C7 from the crack. It would not make sense for the other side of C7 to also be a ground, it must be some voltage that the crack separated from that one round solder joint. Would have to look at both sides of the board to be sure. My opinion, use advice at your own risk.
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