A couple of weeks ago my hard drive decided to kick the bucket. Yep, one flash of the screen and it was dead as a dodo! Now, as I'm trying to sort things out on my new hard drive, which had a "mirror" made of my old setup made for it, I've found some of my programs are corrupted, one of them is Skyrim. Mod Organizer is still there, as are all my mods and save games, but when I try to boot-up Skyrim nothing happens. Mod Organizer disappears as usual then nothing. I tried booting the game up via the SKSE icon on my desktop and an error message popped up saying that I'm missing the following file:

X3DAudio1_7.dll

Any ideas?

have you done a game cache verify? You will have to reinstall things if files are corrupted.

Try reinstalling the DX runtimes. http://www.microsoft.com/en-us/download/details.aspx?id=35