I need monthly 2002 precipitation data for Argentina. Where should I look?

The Global Historical Climatology Network will have what you need.

http://iridl.ldeo.columbia.edu/SOURCES/.NOAA/.NCDC/.GHCN/.v2beta/

Select the "Searches" link next to the map- this will bring to a page where you can search for stations via their country code (Argentina = AG).