Dude you gotta Dell !
Check your BIOS to see if the On-Board sound is ENABLED.
Try a different set of speakers to rule them out.
If the driver is correctly installed and the speakers are fine then your sound card is more than likely shot. Go to any computer store and buy a PCI (white slots on MB) soundcard. After the card and software are installed, make sure you go back into the bios and DISABLE the On-Board Sound. Even though it is dead it is still has an IRQ set to it.
You should have no problems afterwards.
If you have anymore questions Email me. I am always glad to help out.
Oh yea if you couldn't tell my job is computer repair/support related.