The display works independently and will switch on as long as it's receiving battery voltage, so if it doesn't switch on, it's not receiving battery voltage.
If your battery switches off as soon as you connect to the controller, you most likely have blown MOSFETs in the controller. You can confirm that by rotating the motor backwards, where you'd get high resististance to turning, or you can measure the resistance between each motor phase wire and the battery positive on the controller with everything disconnected from the controller, then repeat with the three readings to the battery negative wire. each group of three should be the same as each other and in the range 3k to 24k - often around 7k.