Many times homeowners add these sinks and just run drain lines that connect to the waste line. The absence of proper venting will allow negative pressure to build and keep the water from flowing freely. (The old "finger on the straw" theory) Try to determine if that may be the case, if the water gurgles and bubbles, but eventually goes down. If a clog is suspected, does it affect any other fixtures? Do your toilets flush slowly? The cause could be tree roots growing into the main waste line or a collapsed waste line in the yard. Many plumbers now are equipped with video cameras that are installed into the pipe to determine exactly the location and extent of sewer problems. Good Luck.