Two possible solutions...both require opening up the piping under the sink for maximum effect. Hopefully your pipes screw into the joints; not cemented. Also, making sure the clog is not in any accessible pipe that is directly under the sink.
1. A hand snake device to "snake" out what is clogging you up.
2. The hose trick (shoving a garden hose down the pipe and turning the water on all the way to blast the clog out)
RC
January 2010