It's not clear what would cause that. It could be through-the-air noise. If so, it will vary by proximity. Try moving it far away from your amplifier and see if it goes away.
It could also be that the ground in your computer's power supply sucks. Make absolutely certain you are using a three-prong power cord with your computer. Otherwise, any noise in your computer's ground rail will travel right across those audio lines and into your amplifier (assuming it has a three-prong power cord, which it probably does).
It could be that your power amplifier has a floating ground, in which case you're going to get digital bleed into the signal no matter what you do because there's nothing more than a few kilohm resistor between the ground bus and the input.
Finally, it could also be insufficient noise damping in your computer's power supply and/or motherboard. Replacing the power supply and/or the motherboard with a better one could improve that.
If I knew more about your system, I might be able to give some more specific recommendations. What kind of computer, amplifier, and audio interface are we talking about? Where are they physically located? Does the hard drive share a single FireWire bus with the audio interface, or are they on separate busses?
BTW, I would *not* recommend lifting an AC ground on equipment unless it's for a one-night gig out in the field somewhere. That is always the wrong way to fix a hum problem, though it sometimes does work.
Lifting the ground on the hard drive almost certainly won't work, however. Signals and noise, by definition, always flow towards a ground (assuming your building ground doesn't suck). If you disconnect the hard drive's ground connection, any noise the drive is generating will have no other path to travel but through the FireWire cable's ground shield into your computer, making the problem worse, not better, and potentially causing FireWire data transfer errors that can corrupt data on top of everything else.
If you had to lift an AC ground to solve the problem, the most likely candidate would be the power amplifier, but I emphasize that this should never be used as a permanent solution for obvious safety reasons. The likely path for the noise is from your audio interface through the shield in the audio cables out to your amplifier. If you need to lift a ground long-term, lift that shield. Unlike lifting a power ground, there are generally no significant safety risks associated with lifting an audio cable shield.
Oh, and ideally, if you lift a cable ground like that, you should provide an alternative path with a heavy gauge copper wire between a grounded part of your audio interface (the shield on an unused input or output, a case screw, etc.) and your amplifier (the shield on an unused input or tape output, a screw, etc.). This will ensure that you have consistent ground potential across the entire setup, but because the wire is physically not adjacent to the wire, it won't induce noise in the audio signal.
That said, my money is on the hard drive sitting on top of the amplifier or something.
