I don't really see your sound card in there at all! Normally you would see something from Realtek, or Sound Blaster, or Turtle Beach, or something with "AC'97" in the name. But I don't see any sound drivers if that is your whole list. Hmmm
Do you have a sound card, as in PCI, or is it onboard? If you're not sure, look at the back of your case where the speaker plugs are. Are they on a horizontal card about middle of the case or lower? Or is in up higher where the rest of the plugs are? That is onboard. PCI is down lower in a sloted area.
If you have a card, I would open the case and make sure it's still plugged in tight. If you have onboard, I would go in the BIOS and make sure it didn't get turned off some how.
If it's a card, you could turn the PC off and move it to another slot.
Once you checked the physical stuff and BIOS. Go back in Windows and run the add new hardware wizard to see if it finds your card. That is, if Windows doesn't automatically find it after you changed things.
Lastly, sound cards CAN just die, it's not impossible. So maybe if all else fails you can find a used sound card at a local shop, or buy a cheap sound card. Shouldn't cost more then $25 for a cheap sound card, see if that works.
Good luck.