From what I saw at Dell, your motherboard uses an ADI audio device (not Realtek). The Dell suggestion makes zero sense. You would still need drivers in the end and you can't upgrade from XP to Win 7. That transition requires a clean install.
Not that I advise it, but you can go from XP to Vista to 7 (all have to be 32-bit or 64-bit, no mixing) on an upgrade path...but I digress.
Restart your system. Access your BIOS. As I recall, you can initiate some on-board diagnostics that should be able to verify that we aren't dealing with a hardware failure. Also, while in the BIOS, you should verify that the audio adapter is enabled.