If you go into Control Panel, then Systen, then Device Manager, you gan usually see which sound card you have. Then you can locate the driver. You may have to pull the cover and look if it's a card-slot device rather than an integral-to-the-motherboard piece.
But, I'd start with contacting Gateway with the serial number. I don't know if they can do it that way, but many can- I know Dell does.