I am trying to remove my bathroom vanity, and I need to shut off the water to my bathroom sink. The valves under the sink, for some reason do not turn. They have no rust or corrosion on them. They just won't turn by hand at all

Put dish under valve and loosen packing nut a little, about a 1/4 turn to start. Dish to catch any water from nut. Then try by hand again. If not use a 2 pliers. One on valve body and the other on stem.

Chuck

Chuck pretty well nailed it! The only other option would be to shut the water off to the house and replace the angle stops. Good luck, Tom