"Venetian blind" is a broad term for most horizontal-type blinds. Most blinds function in a similar way, and the problem with sticking or not opening properly generally is associated with a malfunction in the head rail of the blind. The head rail is the area where the cords are located, as well as the rod that controls the opening and closing of the blind.
Release the Cord Lock
Pull the string on the blind from side to side to see if it will release the cord lock. The cord lock could be stuck, preventing the blind from working. While the blind is still in the window, take a flathead screwdriver and place it into the cord shaft in between the little metal strip, and push. The metal strip should release the cord, allowing the blind to move up and down. If the blind is still not working, take it down and look inside the head rail.
Look inside the head rail to see if the string is caught on something, causing it to be stuck, or has shredded, or if the steel rod in the center has popped out of place.
Fixing the Problem
Place the steel rod back into the holder if that was the problem. If the string was out of place and stuck on an object, release it and put it back into place. The string may also have shredded or broken completely. If this is the case, the blind needs to be restrung.