Toilets, Sinks, Showers, Tubs and Disposals - Kitchen faucet slow to start

I posted this as a reply but discovered that I should post this as new. I have the same problem as davibrew but with a two-handle kitchen faucet. It does not matter whether it is the cold or hot side turned on. What makes my problem so strange is that I have tapped into the hot water side above the shutoff valve to run a bar faucet out of the fourth sink hole to run a portable dishwasher. When I turn it on it runs full force. I have pulled the strainer and ran the faucet without it and it still acts the same starting with a dribble and slowly building to pressure. I have in the past replaced each valve assembly so it seems strange that this faucet acts this way. Any help would be appreciated.

The only other part of a kitchen faucet between the hot/cold valves and the spout is the diverter valve for the sprayer. Perhaps that is hanging up and not returning to its proper position? The DV usually sits below the spout and is typically removed by unscrewing it. Try removing it and see if the faucet works as it should (of course the sprayer won't work with the DV out!). Might need to replace the DV assembly.