Some computers have a little device on the motherboard that looks like this:
12-201-032-TS.jpg
It may be that your computer has one of these and it has burned out. It has been a long time since I have had a computer with one of these on it and I don't remember if it played sounds or not, but I going going to assume it did more than just play generic system sounds.

You could always run to Goodwill or something and pick up a set of speakers for less than $10 if you want something you can see.