Strange A/C problem - 2004 Honda Accord LX

Check this, look for the heater control valve under the hood, the one in the heater hose just before the firewall where it goes into the heater coil. With the heater control all the way to cold, see if this valve is fully closed. Have someone turn the heater control from hot to cold and then see if you can move it some more. If you can, then the AC should work as long as you don’t turn the heat back on.