Unfortunately what you have described indicates that your problem seems to be with the main circuit board it is not getting the power supply properly may be the battery contacts are defective please check them if they are ok then repair the camera because the repairing is not possible at home.
1. Remove the battery and memory card from the camera. Mechanism 2. Let the camera sit with the battery and memory card removed for approximately 20 minutes. 3. Clean your battery contacts with a clean cloth. 4. Reinstall the battery and power on the camera. If your camera still doesn't turn on, unfortunately, your camera will require service to correct the problem. I apologize for this inconvenience.