There are few reasons why the air conditioner may not turn on, so let's talk about most of them in detail. The most common reason is that the batteries in the remote control are dead. At the same time the display on the screen may work. Let's try to change the batteries. Also, every air conditioner has an emergency on button. If air conditioner switches on when you press it, this means the problem is in the remote control. If it is not, then we are moving on.
Also conditioner is not able to switch on because of the absence of tension in the network. If conditioner has a cable with a plug, then try to plug any other appliance into this socket. It is not recommended to use a gadget charger as a test, as the mains voltage may be low. Often this voltage may be enough to charge the phone, but not to start the air conditioner. If it works, then move towards the air conditioner. If not, then move towards the circuit breaker. If the socket is not working, try to start the air conditioner through an extension cord, from another, working socket.