First off, clean the surrounding area. Lots of opinions on how to do this, but the poor mans way would be to first use a high grit sandpaper and lightly sand the corrosion off. Metal should like nice and shiny, not dull or burnished. Be careful not to further ruin any traces of course. Then, using a mixture of baking soda and vinegar and a rag or toothbrush, clean the surrounding area and dry. Next, using a DMM, test for broken traces and continuity. Solder accordingly.
