According to pulse audio, sound is playing, but it isn't
 

Despite the bar below "HD-Audio Generic Analogue Stereo" under the outputs tab in pavucontrol moving around indicating sound should be playing, I can't hear any audio. My soundcard is being detected fine, I have the modules I need for the sound card loaded, pulseaudio seems to detect everything fine (and so does alsa), everything appears fine in pulseaudios configuration file, so as far as I can tell everything should be working. It's not an issue with the headphones because they work on my phone just fine. Not really sure where else to look for an issue. Any help would be appreciated. Also, I'm using Gentoo (and have checked my use flags so there shouldn't be any issues there).

What hardware?

Are you sure the correct port is selected?

In pavucontrol, I have under "Output Devices", a device "Built-in Audio Analog Stereo", under which is a drop down for "Port" containing "Speakers" or "Headphones (unplugged)". If I select "Headphones (unplugged)", the bar in pavucontrol will still move with the audio level, but obviously, no sound.

The builtin sound card is a "SupremeFX S1220A" (From what I have read it's basically an ALC1150 and even uses the same driver from what I know). Also I'm certain the right port is selected. I even tried to do simultaneous output to all sound cards and still nothing.

i recently had the same problem on a laptop with debian, and it happened after resuming from sleep.
i had to go into 'alsamixer' and fiddle with the controls (Auto Mute iirc) to get sound, but evtl. the problem came back.
now i haven't had it for a while, knock on wood.

sorry i can't be more precise, this happened at work where i had no time to analyze what i'm doing.

I FINALLY have had some progress in finding out what the issue is with my audio, it seems that if I first start pulseaudio and THEN plug in my headphone sound seems to work perfectly. I didn't notice this because I only really ever use my headphones at my PC and so they are usually in there when before I start my PC. So it seems like it's a different (although possibly related) issue I'm having compared to yours :)