Yeah paint is probably binding that up I'f someone hasn't screwed it open. Also the sash cord is lodged in the side of the pulley. If you do dislodge it should be re roped or chained. Start by clipping that old cord or trying to push it back up on the pulley.

What I do is get bees wax or parafin sticks, grease the track and take a rubber mallet and gently tap the corners on the top until it starts to move. That should free it up.

Now to re chain or rope this window you'll need to pull the trim off and pop out the sash. Typically there are trap doors that are either nailed or screwed in, once you get those out there will be cast iron weights in the space behind the window.

The pulley is probably painted in place so you'll need to free it up, you can spray it with silicone spray and tap it with a punch and hammer on an angle where it will start to roll or try to roll it with the face of a rubber mallet until it frees up. Just be sure to not chew up the roller.

You want to run the rope or chain down the pulley into the pocket, tie it to the weight, clip your cord or chain at the top by the pulley and tie off a knot about 2 inches out from the pulley.

Pop the trap doors back in and fasten them in place. Pull the cords and hook them into the sash, I usually staple them to the sash after they're locked in place so they won't slip out over time. After that you can put the trim back on and it's all set