These two capacitors are known to be bad for so many hundreds of people. If you take the monitor apart you may as well change. It is only $5.00 max. Even if they look good they cannot be trusted.
The first time I saw Win95 my jaw was on the floor. I bought a copy. It was amazing to launch the CD and see it install with everything working right the first time. They did an amazing job with Win95. Remember the launch party with the Rolling Stones - Start Me up?
Hardware issues are best diagnosed by the moving/replacing parts until the problem is isolated. The biggest issue is if you can repeat the failure reliably. If not you can never be totally sure if you solved the problem or not. I would start by looking at the power connectors where they plug...
M LG Flatron L246 had same problem. Was bad caps. I made a video on how to repair:
http://www.youtube.com/watch?v=qJhkLiMR12g
There were two 3300uF 10V capacitors that were bulging.
It's called the Arrhenius Equation:
http://en.wikipedia.org/wiki/Arrhenius_equation
The hotter they get, the faster they fail. I would guess 1/4 to 1/3 of all the video cards I have got in last 5 years have failed. Seems nVidia is a bit better than ATI but not perfect.