Cheap audio (ie. game) cards are not well known for their ability to reject picking up high frequency interference from nearby components. You may want to reposition your cards in their ISA slots to determine if this noise is related to a card next to the sound card. In particular, keep the sound card away from the video or HD controller cards. If possible, leave the two ISA slots next to the sound card empty.

You may even want to consider constructing some extra shielding around the sound card. What you do is get 2 thin pieces of copper or aluminum sheeting approximately equal to the width/height of your sound card. Glue a thin piece of cardboard (ie, cut up a shoe box) to each side of each metal sheet. (ie, You want to sort of encase each metal sheet in cardboard so that it doesn't make direct contact with any nearby components, including on the sound card). Place these 2 shields around the sound card (ie, one on each side). Connect an insulated wire from each shield to the chassis ground. Furthermore, you should make sure that your audio amp is plugged into the same grounded outlet as you're using for the computer. Also, use shielded audio cables to connect your card's audio outputs to the amp, to avoid picking up any noise from the ISA backplate connector (which touches all of the cards in your ISA bus, and could possibly transmit noise between them. But hopefully, your card uses some sort of molded, plastic insulation around the output jack itself, so insulated cables are just an extra, probably unnecessary precaution).

But I doubt that any of the above will help you if the noise problem is a result of the sound card's own generated noise from using parts with low Signal To Noise ratios. You can't make the components do more than they're designed to do. The above shielding will only eliminate noise that isn't supposed to be inherent in the card's design (ie, noise resulting from interference with other cards). The shielding won't make poor components on your card perform better than their design allows.

The biggest source of noise in cards is a poor analog output stage and/or poor analog input stage. When you're not using the Line Input on your card, turn the volume all of the way down. Also, use the Line Output of the card and run it to your own powered speakers or amplifier. Avoid using the Speaker Output on the card.