We had a similar problem at one of my first jobs where I was a programmer and backup network support guy. One employee was having a problem with his CRT monitor flickering. It was very subtle, but just enough to drive him nuts.
So we replaced the monitor with one that worked fine on another machine. Same problem. We tried replacing cables, power cords, and did a bunch of other troubleshooting things. Problem persisted. Eventually we replaced his entire computer. Same problem.
Finally I put his computer and monitor on a cart with an extension cord and wheeled it out into the hallway. The problem went away. It turned out to be bad electrical shielding in his office.