Mac Mini: No sound except for startup chime

Solution 1:

Try this https://apple.stackexchange.com/a/54800/210364

I had the same problem, and these steps helped:

Reboot your mac holding Command + Option + P + R until you hear at least two startup chimes.

Solution 2:

So after a long, long time without any sound on my computer, I finally fixed the problem! First I booted the mac into recovery mode by restarting it while holding ⌘ + R. Then I simply chose Reinstall OS X from the OS X Utilities window. Then after a while of installing, the machine worked good as new!

Hopefully this helps anybody with the same problem in the future!