Are you SURE that you have built-in speakers? Most desktop computers (99%) do not have built-in speakers.
The wires can be just twisted together and taped for testing. Be sure that the same colors of wire are twisted together. Test and see if you get sound. If it works, then you should untape the wires, solder and retape.
If it does not work:
It is still possible that the speaker's amplifier was blown when the wire was originally cut.
I assume that your speakers have an amplifier which is powered by something that is plugged into the wall.
You can test powered speakers by plugging them into the earphone connector of a portable CD player or radio.
You should hear music/sound from the speakers.
No music/sound:
Time to buy new speakers.
..
I have an AMD DURON tm 1.10 ghz, 224 mb of ram, Windows XP Professional version 2002, Service Pack 1.
This is a desktop computer. I don't see any wire coming out of the monitor, so are the speakers in the CPU? The sound card is VIA audio driver. What is the proper way to splice wires back together? My husband used some kind of connectors, but the wires came apart. Should they just be twisted and taped or soldered? I really appreciate the help. Thanks

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic