If the water pressure at the kitchen sink is low will this affect the function of a dishwasher? My dishwasher goes through all of the cycles but it doesn't seem to fill up with enough water and also the washer cycle doesn't work. Could this be a result of the low water pressure?

It could be. Don't run any other water (bathtub, washing machine, etc.) when running your dishwasher. See if that helps. What elevation do you live at? If you live on or near the highest point surrounding your local community that can result in low water pressure.