Mark,

If you have access to Cedar De-Noise or maybe some of the waves stuff, you should be able to sample the computer noise and reduce it some. Or maybe you could record the sound of the computer alone and flip in out of phase to see if it will go away without harming the voice….

Thanks. I actually have the waves gold bundle, but haven't used the de-noisers...any tips?

Yes, Doug is right, Cedar de-noise and Waves denoiser are great tools.
There are also some other alternatives: cool edit pro and a few wave editors have a de-noiser. Tough they maybe not top of the line, they are usable, and some are not too expensive. So if you have budget considerations, it might be a good avenue.
Of course, the first thing to do is to record (get a sample) of noisy material, without the voice, so the program can analyse it. Usually, you can easily get this sample either at the beginning or the end of the recording. You can also get this sample in between spoken words or, even better, pauses. To do a good job, you need, in my opinion, at least 1 or 2 seconds. Then the program will analyse this noise and, hopefully, do a good job in removing it.

It is generally a good idea to try different settings in the denoiser. First, you need to make a back-up of your original track. Then try different percentages of noise removal. If you utilize extreme settings (because you will want, like everybody else, to remove it all!), you might get unpleasant artifacts. But if you can remove, lets say, 75% of the noise or more, it will sound dramatically better. Depending on the situation, a bit of residual noise could be acceptable, and you will not get these nasty artifacts.

Also I’ve found at least with the Cedar that multiple runs with lower attenuation levels (bring noise sample down by - 2 or 3 dB) is smoother and leaves less artifacts than 1 massive reduction.