The key spins a strike bar. Spray this area well. Try pushing on the handle when trying to turn the key.
Slide the key in and out several times in case the pins are stuck which is probably the most likely issue.
If you have to, you can drill out the lock and then just replace the tumbler. Drilling out just the tumbler will not effect the operation of the handle and the hasp. The actual operation of the strike mechanism is controlled by the operation of the handle.