Once you pass the cranes in this location, the birthday key will be yours.
Diggy needs to push the three red buttons in the first room. To reach them all, clear all possible tiles first and he will reach the entrance to the second room.

If you pass the first room with the cranes, in order to proceed, Diggy needs to move the cranes with the following set of buttons:

Well and here is the last puzzle with cranes. Just push the buttons into the following final position and Diggy will be able to collect the reward!

Thanks, designer Ivan 😊.