It's perfectly plausible. There will be a controller chip that hooks them into the PCIE on the board. If the controller chip dies so do the things on the end of it. I've heard of sound cards or NIC dying but not usually both. Check the capacitors around where the chips are, and look for any burning on small chips in close proximity.
Could be a component within the PCH is failing. This would handle Ethernet and Audio among other I/O functions.
Before mess-arsing around with that, why not do as @Ice Tea says and boot into Ubuntu from a USB stick? If the sound works there, you know your hardware's fine and can mess around trying to fix Windows at your leisure; if it doesn't, then your hardware's chuffed.
If it isn't hardware, I'd be extremely surprised. Have you tested every USB port/header, both internal and external? They're also controlled by the PCH so any errors there would confirm hardware.
't'ain't hard: make an Ubuntu live USB, reboot your computer, wait for Ubuntu to load, see if you hear the drum sounds on startup and whether you can load YouTube in Firefox. If you can, Windows is shagged and your hardware is fine. Yeah, you're gonna need access to a system with a 'net connection to make the USB stick - which could be a problem if that's your only PC and you're posting from a phone or tablet. Could also go to the nearest newsagent and pick up a Linux magazine with cover-mount DVD, I guess...
You could do all that on mine, and it's a five-year-old AMD A10-5800K with no discrete GPU. Hell, I do do all that, except play WoW.
Yep! Like Gareth said mate, it's really simple and as all basic drivers are built into Ubuntu, no sound or no network = hardware issue.
