I feel like I am stating the obvious, but I don't see where anyone has mentioned it yet. I am going to assume that you have double (and triple) checked the 'Duh! factor' things like the connection from the sound card to the speakers (are you sure the speakers are not plugged into the microphone jack or something?) and making sure that the OS volume control feature is not turned down or muted. Have you shut everything completely down (and powered off), unplugged the PC's power and speaker's power, plugged them back in and booted back up?
If these are fine, then there are two major possibilities: speakers have gone bad, or like others have suggested, the sound card (integrated or not) has gone bad. If you can, try a different set of speakers or headphones (borrow from a friend if you don't have an extra set). Or, try the speakers on another PC, portable CD player, vintage Walkman from the 80's, etc. - anything that has a standard mini audio plug. Better yet, do both just to eliminate the slim possibility that you have had a double failure and both have gone out. (Believe me, it can happen.) Before buying a sound card and installing it, just to find out that the the problem is the speakers, it is worth trying these simple steps.
And yes, it is possible to get both sound cards and speakers too for around $7 each or up to and exceeding $200. But, if it was me, I would not spend less than $30. You should be able to get something of at least semi-decent quality for around that price.
Good luck.