The switch starter on the tube is generating electromagnetic radiation which is being picked up by your monitor and modem and interfering with them.
This kind of probelm is faily common, you can buy special filters to connent in series with the appliance making the noise, but this might be of limited use if it's being radiated rather than conducted.
Another option might be to consider buying an electric starter for your tube, this should solve the worst of your porblems but it isn't a complete fix.