Q.Sickly Holly Bushes
We two holly bushes planted near each other that are about 10 years old. Both of them look very sickly for the first time. Many of the leaves did not come back after the winter and many of the existing leaves have brown areas covering 10%-70% of the leaf surface.
How can I identify the disease or pest that is causing this problem? All of the other plants nearby look great. The problem seems to be confined to the two holly bushes.

Your sickly holly bushes probably did not succumb to disease or pests but rather to old man winter. It sounds like your hollies got winter burn - more information on winter burn can be found here:
https://www.gardeningknowhow.com/plant-problems/environmental/winter-burn-in-evergreens.htm
You will want to treat the cold injury in your bushes via judicious pruning (of the dead and damaged parts) and making sure it stays hydrated. More information on cold injury and pruning can be found at the links below:
Winter Damage Of Shrubs: Types Of Cold Injury In Shrubs
https://www.gardeningknowhow.com/ornamental/shrubs/shgen/winter-damage-of-shrubs.htm
Cold Weather Damage To Trees – Pruning Winter Damaged Trees And Shrubs
https://www.gardeningknowhow.com/ornamental/trees/tgen/winter-damaged-trees-shrubs.htm
Trimming Holly Bushes
https://www.gardeningknowhow.com/ornamental/shrubs/holly/trimming-holly-bushes-how-to-prune-holly-bushes.htm