As to dxdiag JW it'll show you a list of tabs, one should be titled Sound, or "Sound 1" "Sound 2" if you have more than one soundcard...ie: onboard audio as well as your slot in card. Theres a test button under the respective tab and it'll play sound via the card and ask you if you heard it, yes or no button to hit, cant recall what happens if you hit no tho.
Still thinking on it being summat daft if all you've done is move a pc from "A" to "B". I dunno if you have, like myself, a subwoofer box and by default more than the average wires. Thinking back to anytime I've lost sound thats been the culprit, a simple audio jack not seated properly, or my usual ...the audio lead jack stuck in the wrong hole at the back of the Soundcard lol
Pop in an audio and set it playing with the volume turned up, then nip round the back and play about with the wiring whilst its playing...on the chance that'll burst into life.
Having a red hot cuppa in your hand at this point is not advised 