We have a 2 handle bathroom sink that when you turn on the cold it has a very small amount that comes out and them stops within a 1/2 second. We turned the water off at the valve under the sink and cleaned the line to the faucet, but there was nothing in it. I then turned on the valve under the sink with out the line connected and NOTHING came out. The pipes are behind tile in out bathroom. I would love to find a solution to this problem with having to knock out the tile behind the sink. I believe my husband tried to back flush it, but that only caused the bathtub's cold water to stop. Anything you could offer would be a great help. Thank you

It sounds like you have problem with your angle valve, you have to shut off water to the house, remove the packing nut on the angle valve see the image below, once the packing nut is removed check the stem and the washer for any damage, you may need a new washer or new angle valve, good luck.

John