Making PC Quieter to the Mic is probably cheaper.
I have seen people with noise issues like this use as simple as a paper plate behind the mic so that noise cant get to the mic from the computer that is on desk, the paper plate acts as a noise barrier. However if you have a small room and a really loud PC, then you may want to relocate the PC or if the noise is not a normal operating noise fix this noise issue with the pc.
What specifically on the pc is making noise? Fans? Hard Drives? etc?