The water flow from the kitchen faucet went from flowing really slow to nothing. We removed the lines and there was a lot of calcium deposits. We cleared all of the lines and it still didn't help, so we changed out the entire kitchen faucet and it worked great for one day. After we ran the dishwater last night, the water pressure slowed and is down to just a trickle on both the hot and cold side. BTW, the water comes out of the wall fine. Is this a dishwasher problem or what? We are baffled.

There is likely an aerator/screen on the faucet outlet. Remove it and let the water run for a minute to flush. Clean any sediment caught by the filter screen. If it continues to plug, you might consider an inline sediment filter to trap particles before they reach the faucet.