Nine times out of ten, when your dive computer is not turning on and you are questioning why it is probably because the battery needs to be replaced. However, you need to remember that there are various other internal components that can go bad and a new battery is not going to fix the issue every single time. For example, the pressure transducer that is used to gauge the depth and barometric pressure of the water could be going bad. But, the device will still turn on in this case; it is just you may be receiving error messages.
If the dive computer is completely unresponsive even after you put a new battery inside, chances are something else is damaged and you may have to see a professional.