Well your speakers themselves are irrelevant to the equation as long as they actually work, it's rare that speakers just up and die without some kind of horrible noise (although, if these are speakers you haven't used in a very long time, it's always possible). Open up your device manager (Right click on 'My Computer' > 'Properties' > 'Hardware' tab > 'Device Manager') and see if there are any devices with a yellow exclamation point. It will automatically expand any category with an error in it. If there is an error, I hope it at least recognizes the device that isn't working properly, if it doesn't and gives you a generic 'PCI Device' or the like, then you're going to have to yank the card and look for the serial number. Alternately, if you don't have a sound card and instead have onboard sound, the model number of your motherboard should be enough to figure out what sound card.
Now, if you have no devices with errors expand the 'Sound, video and game controllers' category and see what it has down- you will probably have all or some of the following: 'Audio Codecs', 'Legacy Audio Drivers', 'Legacy Video Capture Drivers', 'Media Control Devices', 'Video Codecs'. Anything not on that list should be your actual sound card, for example the motherboard I put in this machine at work has 'Realtek High Definition Audio'.
