No audio output from motherboard running Linux Mint 17.1

I'm not getting any audio output in Linux Mint, to my headphones. I'm pretty sure it worked in Windows 10 before I installed Mint, so it's almost certainly a software issue.

So far, I've tried both the rear and front headphone ports. Yes, the cables are plugged into the correct jacks / sockets / ports! I've tried borrowing someone else's headphones and they didn't work either.

When I go into the Sound settings in Mint, there are 3 options under the Output tab for devices to "Play sound through". A 4th option for Headphones is listed when I plug headphones into the front audio jack. I've clicked the "Test Sound" button for each of the 4 options, and tested both left and right sides, but with no sound at all.

The first option, being "HDMI/DisplayPort HDA NVidia" appears to relate to output through the video card HDMI cable, so I don't think that's the one to use. There is a "Digital Output (S/PDIF)" option, and I don't think that's the one to use either. The remaining options "Analog Output, Built-in Audio" and a Headphones option should probably work depending on whether the headphones are plugged in to the back or the front of the PC. Neither works though.

Under the Sounds settings Input tab, the Rear Microphone shows audio input being received by the mic on my headset, so that much is working.

I've tried a few other things as well that were suggested on the web, such as running "AlsaMixer" and activating channels, reinstalling some apt packages, etc, with no luck.

Any ideas for how to proceed would be much appreciated.