Putting the computer on something to absorb vibration may help, if it's using the empty drawer as a resonator---your suggestion sounds very likely to me---even something like a neoprene mouse pad or a couple of cut-to-size bits of the thin rubber webbed mat you put under scatter rugs to stop them scattering might have an effect. I sympathize very much, that kind of low-level drone can be very stressful. Computer fans are the bane of existence.