I have a shrub that has a lot of leaves and branches covered with white capsules. They brush off and do not move, so I think they are eggs. I don't see any live insects that are in the same numbers as this many eggs would produce. I introduced some lady bugs and they didn't seem interested in the white capsules. Could you help identify them and provide any remedy?
This is an infestation of a type of sucking insect called scale. This particular scale is called "Euonymus scale". (Your plant is Euonymus)
Here is our page on scale: https://extension.umd.edu/hgic/topics/armored-hard-scale-trees-and-shrubs
and our page on Euonymus Scale itself: https://extension.umd.edu/hgic/topics/euonymus-scale-shrubs
At this point we'd suggest either removing it or cut the plant back to the ground and let it re-grow. Keep an eye on the new growth and treat as needed.