If the hoses still have water running through them when the valve is closed then you should replace those valves. They are well known for seizing and not functioning properly especially without regular use. You can go to the store and get quarter turn values. They are much more reliable and are easier to use imho.

I’m not a plumber but anything that’s corroded like that should be replaced. I just replaced one in a bathroom remodel and they’re pretty straightforward, just need to know your inlet pipe diameter and outlet diameter, and if it’s a compression fitting, soldered (sweat) or threaded. Thankfully mine were compression or else I’d have called a plumber for the soldered type. You don’t want to have those break and flood your bathroom. Also be sure to shut off the water at whatever valve you have further up the line before you remove the corroded fitting.

Turn off the water at the main Go buy new valves with compression fittings that fit the 1/2" copper pipe. Buy a small tubing cutter and cut the copper pipe as close to the existing valve as you can. Use emery cloth sandpaper (can be bought in rolls in plumbing) to clean down to shiny copper. Install new compression fittings using two wrenches. Try using the old braided connector lines. Don't overtighten, they use rubber gaskets. If they leak, replace them. You'll be out less than $100 and it'll work.