I've just installed Ubuntu mate on an old Dell Inspiron desktop. I get sound fine out of a pair of USB headphones, but if I plug my speakers into the built in sound card (headphone socket) I get nos sound from the speakers. Looking at the hardware profile in sound references, it shows built in hardware is disabled and the only available profile is "Off".
Any ideas how to turn it on, or am I going to have to buy a sound card?
I have a similar issue with a Dell Precision M4800 notebook. According to https://bugs.launchpad.net/ubuntu/+source/alsa-driver/+bug/1786495 it is somehow related to recent NVidia drivers messing things up audio-wise, although I also have the problem occasionally with the older 390-series drivers (with 430-series drivers the audio output jack basically never works).
Also, the supposed workaround listed there did not work for me, so I got a cheap USB audio adapter which works fine.
Can you boot from a live USB / DVD and check if audio works there?