Macbook turns off after a minute – not in safe mode, but in all recovery modes
I would test booting from an external drive running a clean installed OS. If the problem persists, then it's almost certainly a hardware problem. If not, then you are in a good place to repair the issues on the internal disk.

It is odd that Safe Mode works, but Recovery doesn't. I presume this is without the audio hardware attached? What is the audio device? Does it require drivers?

It is certainly worth trying to install the Mohave update (or a Combi installer for maximum restoration of any corrupted system files).

Failing all of this, I would take it to an Apple Store. It might be out of warrantee, but they can still diagnose and fix problems. It's possible, depending on your location, that statutory consumer rights may supersede Apple's own warrantee, if it is a hardware fault.