This doesn't sound like a capacitor issue unless there are SMT electrolytics that have leaked out on the board.
Does the Color Classic use the RPM control pin on the SWIM to control the monitor brightness like the Classic does? If so a good start would be monitoring brightness control line to the monitor board.
Does the Color Classic use the RPM control pin on the SWIM to control the monitor brightness like the Classic does? If so a good start would be monitoring brightness control line to the monitor board.