Update

The plumber came today and put in our new faucet for us. He had a pretty bad time getting the old faucet off. That made me a little happy, since I would've felt bad if he'd walked in and got it off without any trouble. So we're back to hot and cold running water in the kitchen now. Woo hoo!

Now I just need to clean the sink. The new faucet's so new and shiny that the sink looks like crap.