Yes, I disabled the Onboard audio and tried a different PCI slot. I didn't assume it would work, as there was no trouble with the slot in XP. And indeed it was exactly the same. I booted back to XP and it saw the card in the new slot and installed the drivers for it. I'm going to go ahead and...
I've got a problem fairly similar to the OP's. My PCI sound card is a Creative SoundBlaster Audigy SE, and it was working fine in XP with the on-board disabled in the BIOS. I am now dual-booting with Windows 7 (x86) and Windws 7 simply doesn't see that there's any sound hardware attached...