Look in Device Manager for any driver errors. If no sound device is listed at all, and no "unknown device" error is shown (denoted by a question mark) the sound adapter has probably failed.
There are two drivers showing up in the sound devices. One is called High Definition Audio Device and the other is Realtek High Definition Audio. Both of these have no errors on them, however it says "No speakers or headphones are plugged in", even though there are built in speakers and there is an x on the volume control button.
I've tried using headphones, which still doesn't work and there is no audio on my TV when I use a HDMI cable to connect it to my tv.
I read somewhere about maybe the chipset driver being the wrong one but I'm not sure how to change it.
Ok, I now know it's not the sound adapter that's failed as I've bought a USB plug and play sound card which still has not fixed the issue. This is really frustrating as this problem is a regular occurrence and i've done literally everything to try to fix it.