[pathfinderfour]

You have two separate problems. The faucet is a supply problem; and the dishwasher backing up is a drain problem. Assuming that your dishwasher drains into your garbage disposal, and is backing up there, try pouring liquid plumber down the garbage disposal and/or the kitchen sink and following the directions on the bottle to clear that drain. If that fails, you may have to disassemble the drain from the disposal and run a snake through it to try to clear it that way.

Now ... Your faucet stopping is another matter entirely. Either your supply line is clogged up with sediment, or your faucet is clogged with some other kind of foreign matter. It could be a washer has deteriorated and plugged it up. How hard is your water? How much lime and other "stuff" do you have gumming up your pipes? If you're not experienced enough to take the faucet apart and check the washer(s) and the inside of the supply line, then you better call a plumber and get your checkbook out.