how to repair the kernel panic?

Did you figure out how to repair the kernel panic?

Here's my story:

MBP 13in mid 2012

SSD one partition El Capitan, one Bootcamp (can't boot into either)

Battery dies, on reboot I get a kernel panic

Tried reinstalling El Capitan through Recovery (Really vague error, "Error: Please run application again)

Tried First Aid, and got the same error Polinkk got

Even weirder, the recovery partition is sometimes in El Capitan, but sometimes it opens up the Mountain Lion recovery partition.

Apple Hardware Test also says everything is fine.

Any help would be greatly appreciated.

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