Sounds like a problem with the faucet. Most reputable faucet manufacturers (Delta, Moen, Price Pfister etc) have a customer service line you can call in to and they can walk you through trouble shooting the faucet. I can't recall specifically, but I might have had a similar problem to this in the past. If you have a sprayer, the faucet has a little piece in it that moves up and down when you turn on the sprayer so it stops water flow to the faucet and directs it out the sprayer. They go bad and don't move back and forth right, so it may be stuck so you're not getting flow out of the faucet. I called Moen, they trouble shot it and sent me new guts to replace, free of charge.