Removing cornices or any molding for that matter is difficult and must be done with extreme care so that you do not damage the walls or the old cornices. Old cornices can be refinished and then reinstalled if care is taken when they are removed. Care and time must be invested in this job in order for it to be done correctly.
Scrape the adhesive from the bottom and top of the cornice with a putty knife.
Slide the putty knife under the molding and slowly pry the molding from the wall. Take care not to split the board or damage the wall.
Insert the wooden block in back of a nail once the molding is far enough from the wall. Place your pry bar between the wall and the wooden block.
Pry the nails out of the wall one at a time. If a nail will not come out with your pry bar you might want to consider using a pair of pliers to extract it.