Hmm. At this point, I'd try a clean reinstall of the game (meaning, manually delete the Starsector folder from Program Files (x86)/Fractal Softworks, after saving whatever you need from there - the mods folder, the saves folder, etc).
Trying to hunt down and delete any stray OpenAL32.dll/OpenAL64.dll files you might have - likely in Windows/System32 and Windows/System - might also be worth a shot. I'd definitely save those and just rename them instead of deleting - i.e. rename OpenAL32.dll to OpenAL32.dll.backup, or some such. There's a possibility that this is what was causing the sound issues - a different version of this DLL being used than the one that comes with the game.
The initial reinstall is to try and fix the game not running at all after the 2nd reboot, because that's just weird.