Kitchen sink does not drain if we run the water for a couple minutes or dump a large bowl of water in it. It either will not drain at all or extremely slowly. It drains ok for small amount of water. The dishwasher is next to the sink and tied into the same pipe but the dishwasher has no problem draining. We have used roto rooter in all directions from the sink including the vent pipe, but nothing helps resolve the problem. Any ideas? Thanks.

if it takes a minute or more to back up then the partial stoppage is further away than you have been snaking and you have not reached it yet.
the dishwasher doesn't send enough water down the drain to fill the pipe and back-up.

I too agree. You have a partition blockage 10 plus feet into your drain waste. If you don't have the proper sized equipment or if you have a gel'd blockage you will need the proper cleaning head. Chemicals won't help, so if you purchased them, save your receipts when you take the container back.

Lastly, if you are in, over your head, consider calling a licensed professional. A Licensed Plumber.

Best Wishes

"using" a Roto-rooter, is NOT the same as using it "correctly". If you had the drain would be flowing again, unless it is installed improperly, but then it would always have had the problem.