Deciduous thorny bush (possibly barberry)
When pruning the dead branches I found that quite a few branches have a very gold yellow within the bark. Also, when I dug this bush up thinking about replanting, I found many roots were also yellowish. Is this plant dead or possibly have a disease??
Yes, this is definitely a barberry thing! It is common for barberry and their close cousin, the mohonia to Have this yellow inside the stem. This chemical is called berberine, and is a defense mechanism from predators. This coloration is normal and not an issue to be concerned with.
As far as the dead branches... It is wise to remove them, so an infection doesn't set in. Here is another link that will help: https://www.arboretumfoundation.org/about-us/publications/bulletin/bulletin-archive/hidden-gold-internal-coloration/