Kernel panic on a 2012 MacBook Air This is MacBook Air 2012 A1706
Now it doesn't even power on.  It just makes 3 short tones.

Where could be a problem?
The three short tones with a 5 second interval between sets is indicative of a RAM failure

From Apple's support document:  About Mac startup tones


  Three successive tones, then a five-second pause (repeating): RAM
  doesn't pass a data integrity check.


The MacBook Air doesn't have any user serviceable memory, so it's a logic board issue.  Since you cannot boot, there's really no other option but to take it in for service.

It's likely that Apple will want to replace the logic board for a large sum of money.  I suggest looking at a reputable 3rd party repair shop.  I have used Rossmann Repair Group in the past with great success (not affiliated, just a client)

He even has a YouTube video with your exact problem and how he fixes it; it's technical, but full of good info.  Caution:  he's from NYC so his language is typically colorful.