This could be any of several things:
Sound card went south. Check the Sndvol32.EXE (volume control) app - right click the speaker icon in the tray and choose Mixer, or use from Run - and make sure nothing like Wave, WaveSynth, or Master Volume Mute is on. Try putting an audio CD in the CD drive and see if it will play through the analog CD input on your mixer. If the settings look OK, it may be your sound card DAC output or line amplifier is dead. If re-installing the sound card drivers and/or adjusting the settings don't fix it, replace the sound card.
Bad cables or sound card output jack/configuration. Make sure that your sound card is configured for the right speaker configuration. If you have only one pair of speakers, you should not be set for 4 or more. Jiggle the cord in the line-out jack and see if the speakers come on intermittently; if they do, replace the jack or sound card. Verify that the cables between your speaker set and your sound card aren't broken or shorted.
Bad AC feed to the speakers. You test the speakers elsewhere, but maybe the AC plug you use for them at your PC is bad. Try another power strip connection.
Intermittent connection in the speakers. I had to fix one set of speakers where the connector between the right speaker (with the controls on it) and the subwoof cabinet had begun coming loose. I had to get the sub board out, get most of the solder off, clinch the leads properly and resolder tham, and reassemble the whole thing. Then it worked fine.