Your monitor does what is called "mode switching" whenever the video input changes frequencies due to graphics, You have likely noticed it when starting or ending video games, when you are in dos, there are different frequencies depending on the ammount of text graphics or color displayed, I believe that the clicking you hear is your monitor seeking the best settings for the graphics/text being displayed.

It is possable that trying a different video card may remedy the issue, maybe your monitor just conflicts with your card, As I said, I apologise for not being more help. Your monitor does what is called "mode switching" whenever the video input changes frequencies due to graphics, You have likely noticed it when starting or ending video games, when you are in dos, there are different frequencies depending on the ammount of text graphics or color displayed, I believe that the clicking you hear is your monitor seeking the best settings for the graphics/text being displayed.
It is possable that trying a different video card may remedy the issue, maybe your monitor just conflicts with your card, As I said, I apologise for not being more help.