Something is obviously blocking the water. It could be a pinched/kinked water line to the kitchen sink, a shutoff valve somewhere (though I don't think they're common on RVs), or a faulty/crudded up sink valve, or even a foreign object stuck in the plumbing somewhere, probably among other things.
I would probably start by turning off the pump (and city water inlet), disconnecting the connection to the cold water tap on the sink, sticking it in a bucket, and turning the pump on. If water flows into the bucket, you know the problem lies at the faucet itself. You may need a special tool (a "basin wrench") to unhook the water line, depending on how things are set up and what the access is like.