If you want to give life back to a tree - follow Jon Muller's 3D pruning principle: remove dead, damaged and diseased wood. Deadwood can be the source of infection. Remove it and let light back into the tree, encouraging new growth and improving the general health of the tree.
If you are unsure if the tree is dead or alive scratch back the bark. If it is green underneath it is alive; if brown, it is dead. Cutting back after flowering will encourage denser growth and better flowering. Jon's book Plant pruning A to Z - a New Zealand Guide is well worth the investment and available from all good bookshops or his website.
