I've checked everything, but the game won't play sound. Everything else works like a charm. The sound on my system works. The in game sound options are all in order.

Have you already tried running the game as administrator (right-click the game's shortcut => Run as..)?

Also check your sound card's control panel. Restore it's default settings. Especially don't force high quality 48 KHz 24 bit but stick with 44.1 KHz 16 bit, if there's an option for it.