The telephone is “broken”.
When you say “my phone is broken”, your listener might think you just dropped your phone on the floor and now it’s broken (shattered) to pieces.
The telephone is “out of order”.
When something, for examples, telephone, ATM, toilet, vending machine, elevator, etc., is not in working condition, say “it’s out of order”, or just simply say “it’s not working.”
• The elevator was out of order and we had to walk to the tenth floor.
• We couldn’t use the telephone because it was out of order.
When you say “my phone is dead”, it means the battery is dead; your phone needs charging.