how to turn on display without turning on the engine?

Simply turn the car on normally - depress brakes, push "ON" or push "ON" twice. If the battery has enough charge, the ICE (Internal Combustion Engine) will not turn on. If it doesn't, ICE will start and there's nothing you can or should do. It may help in delaying start of the ICE by turning off the A/C and headlights but that's about all the influence on it you have.

I do (vaguely) remember the anxiety but you'll very soon get used to the idea that you do not control the ICE in a Prius, at least not directly while driving. And why would you want to, anyway ?

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Define "power".

The Prius is really just like any other car: you can turn the "ignition" to on without the "engine" being engaged. In the case of the Prius, you can turn the entire car on, so that every system is turned on and the traction battery is delivering power, without the car going to Ready (which means the car will not go into "gear" and be able to be driven).

The normal way you turn the car "on" and have it come to ready is to put the key in (or have it in your pocket) and put your foot on the brake and press the Power button.

To turn only accessory power on (to run the radio and whatnot), have the key in (or in your pocket) and, WITHOUT putting your foot on the brake, press the Power button.

To go further, to turn the entire car "on" without having it come to Ready and without letting the engine come on at all, simply press Power a second time.

To turn it all off, press Power a third time.

Do this all without your foot on the brake, and you'll do what we've been doing with cars for a long time: turn the key to ACC, then turn the key to ON, then turn the key into the spring loaded START area to get the motive power going. But in the Prius, the only way to get it to START is to have your foot on the brake.

If you have not already, please PLEASE read your owner's manual. All of this (and more!) is outlined there. If you don't have an owner's manual, go get one.

Do not press the brake when pushing the Power button. The first push turns on accessories. The second push turns on the rest without allowing the car to go "Ready."

Bob Wilson