That is a very young Picea pungens var. glauca - a blue selection of Colorado Spruce. All the live branches remaining in that area will continue to grow, and will likely cover that currently open spot where you have lost some branches/foliage. Spruce cones are supposed to be beige-y brown, that's normal.
Yes, prune out dead wood carefully - and look for Bagworms or evidence of other insects, pathogens, or cause of damage. Bagworms are often the silent cause of such areas being stripped of needles and leaving "dead spots". The bags of bagworms will be the only thing left by this time of year - and they mimic cones to the casual observer - but the bags from females will be full of eggs for next year's voracious larvae. Removing and destroying them NOW will reduce/eliminate such damage next year.