Well, there's a little problem you are going to have because you say you make components to overlay with graphics in the background. That may work in one screen but it will not work on screens with different sizes. You need to use relative positioning instead of absolute.
About your question, there's a lot of ways to do that, but I'm going to help you with an easy solution:
Create 3 global variables called Button1Clicked, Button2Clicked and Button3Clicked. Set them all to FALSE (the green false you find in the LOGIC drawer
Each time a button is touched, set the corresponding variable to TRUE (again, the green true), and ask IF Button1Clicked AND Button2Clicked AND Button3Clicked THEN open the new screen.