I have a similar issue on a Mac Mini 2010 server. In my situation, the fan runs high and the ethernet port doesn’t seem to work. For some reason, I can’t run any diagnostics on it. Most likely it is a motherboard issue.
I had discovered it was my router that was causing an issue. I have a Synology router and it has a setting called Threat Prevention. It was TP that was blocking any traffic through it including traffic to/from the Ring Doorbell to my phone. Once I excluded the Ring Doorbell, the problem was fixed.
I have the same problem. Macbook Air mid 2012 running High Sierra and ran AHT but found no issues. Under Output it lists Airplay as available but volume icon is greyed out. At the bottom, the Output volume is greyed out and the MUTE button is checked and greyed out. I reseated the internal speaker cable. I tried SMC and PRAM but didn't fix it. I connected headphones to it but didn't trigger anything. I think the logic board is bad despite everything else working ok.
Does the Mac Mini 2010 desktop have the same hardware as the Mac Mini server model? Can I swap parts between the two of them?