Hi Dave. I'm not familiar with the Minime version, but I'd first try with alsamixer in a terminal. Check the volume level in all the devices, and also the presence of MM ("mute"). If everything looks fine, then you could try alsaconf, which will attempt to set up your sound card.
On my laptop, when having sound problems, I'd run alsaconf and it'd display a message saying that it couldn't detect the sound card, so I'd try one of the legacy ones that it suggests and problem solved.
Hope it helps...