[MENTION=476571]JohnFyf[/MENTION] if you are able to take a photo, upload it to something like Facebook, "copy image address" and post it here using that picture icon in the "Quick Reply" box, that will really help us.

Pulling the lever and having the cable move but not any caliper arms eliminates a stuck cable in the cable sheath/housing. It also rules out a malfunctioning lever.

Given those two things, it appears the issue is at the caliper itself. On old bikes, especially lower-end ones, the brakes are cheap and can be pretty finicky to set up or set right after they've been out of adjustment.

If the cable moves and the arms don't, it could be that the lock nuts (where it has the Lee Chi label on the picture you gave us) are tightened too much, thus tightening the caliper arms too much, thus disallowing them to move.

A caliper/pad touching one rim (the other pad way in the air) is a matter of centering the caliper. Loosen the nut on the other side of where the brake caliper mounts, rotate the caliper, and tighten down. As you tighten, the caliper may want to rotate in the tightening direction. This is annoying, but you can overcome that by holding the caliper as you tighten the nut.

Really, we're happy to help, but you have to help us by offering an actual picture of your brakes and/or giving a thorough description (context, which is king), more than what you've given us so far (thank you for at least giving us that much--every bit helps). What is the make and model of the bike?