Okay, well the first thing I tried was simply installing the latest drivers of my soundcard from my motherboard's driver website, that hasn't worked. The next thing I tried doing was uninstalling the graphics card drivers entirely and then reinstalling without the HD audio driver option and then using my motherboard's soundchip drivers. Then I tried going into the bios and seeing if I could somehow enable the onboard audio sound card, but mine only has the options of 'auto' and 'disabled', and auto doesn't work. The error message 'No Audio Output Device is installed' is there constantly (and this answer's Fireberd's response) there IS no speaker option. There is no options at all whatsoever, the listing for playback and recording devices are completely and utterly empty.
Next I tried reinstalling the HD audio drivers from the NVIDEA CD that came with the graphics card and then 4 'High Definition Audio Device' entries come up in the Sound, Video and Game Controllers menu of Device Manager with 4 corresponding 'Digital Audio (HDMI)' devices in the Sound Playback Devices listing, which say they are 'not plugged in'.
After that, I've skipped over the other suggestions I've seen since they were either so hairbrained it left me wondering whether or not they were actually legitimate ways of dealing with this or seemed so dangerous to system stability that I wouldn't touch them with a ten meter pole.
As it is, I have no further clue what to try. Oh and if I haven't stated it already, I do not use the single HDMI port on my video card, neither of my monitors support HDMI and even if they did, none of them have audio jacks or inbuilt speakers.