You want to try a couple things:
1) Power the scanner off an independent 12vDc battery source (the idea is to isolate the scanner from the same a.c. power and phase circuit as the PC). Alternatively, iff you have a PC UPS, run the PC from the UPS - with the UPS disconnected from the wall AC socket.
Now switch the PC on - has the interference gone? Yes/No.
If yes then the noise stemmed from sharing the same AC circuit, and you are going to have to use a filter in the ac circuit at some point, but if not, try this: purchase a role of tin foil and wrap the PC well in a couple layers of tin foil, ensuring no gaps are left open at any point. Now switch the PC on.
Interference should now be gone, or at least substantialy reduced - you may try also wrapping the power cord from plug socket to PC as well, but I doubt you'll realise much in the way of noise/interference reduction. Interference reduction is going to come from wrapping the PC and/or isolating it from the same power source as the scanner.
The question now of course is, just what component in the PC is causing the interference - and it will almost certainly be the power supply as has already been suggested: poor screening, or a poorly laid out ground circuit. You can open up the p/supply and solder in a whole bunch of earth lines, all running to the same point - but quite frankly, it'll be easier to throw it out and replace it with a decent one, or replace the box/tower that the parts are contained in.