The LCD screen is black and fails t turn on, no matter what buttons I press or how many times I reset the camera. What is...

First off, check the battery. Make sure that the battery is fully charged and that it is plugged in correctly. If both of these are good, then the problem could be a faulty power button. This will require some teardown to either check it out or repair it. Refer to this troubleshooting guide for more information: Sony Cyber-shot DSC W730 Troubleshooting