you can get usb speakers that don't need a sound card (well they have a USB sound card built in)
But as you have said old computer and new speakers I would guess that the speakers have never been used with that computer before in which case you need to find the driver disk that came with them and install,that on your old computer.
It's either that or your speakers simply take power from the USB port and as MrBounty said they also need to be plugged into your sound card for the audio.