I need to change this code to start the section of code when the switch is on and not when the switch is released
You should provide a description of your hardware setup as part of your question, as well as a clearer statement of your problem.

Are you saying that your code is backwards, and is acting like the button is pressed when its not, and like it's been released when you press it?

You probably have your button set up as INPUT_PULLUP, and wired to connect the pin to ground. That's a pretty typical setup. In that case the button pin reads as LOW when it's pressed and HIGH when it's not pressed. Just changed your if statement to:

//                         vvv
if (digitalRead(BUTTON) == LOW)
//                         ^^^