Randomly turn on/off... plz give me a good suggestion

We can only give you suggestions or ideas to the extent that you give us good background information. You haven't said anything about the history of the phone, especially leading up to the failure. Was it dropped recently or historically, was the phone recently repaired or did it come into contact with water, even if the phone appeared to survive the ordeal.

You have already changed the battery so that is a good first step. Random failures can be caused by just about anything. You could try to disconnect different modules, one at a time to see if the phone is more stable. Remove the passcode on your device if you have one. Then follow this guide and download 3uTools (www.3u.com) so that it can connect to your device. That way you'll be able to see if the device is on or not even if the screen is disconnected.

Start with the front camera flex, then rear camera, buttons and eventually the screen (that's when you need 3uTools).