When you say cleaned it, what do you mean? Do you mean that you did a factory data reset to the device? I am in Tech support and I solved device issues all day. I have had this issue before come up and it could be one of your apps that you downloaded onto your device that is causing the issue to your device.

Believe it or not there are ugly people in the world that like to miss up other peoples devices with viruses. Your device is like a tiny computer what your computer can get your cell phone can get. The only way to solve the mystery is to put your device is safe mode if your screen starts to work you know that it is one of your apps that is causing the issue and needs to be uninstalled. The other option is to do the Factory reset which will erased everything that you have put on your device so far and will be lost for ever unless you have your device backed up with maybe a gmail acc or your computer or if your provider has something like back up assistance which backs up your contacts and can also back up your media or a memory card. Backup need to be done before any reset is done.If you have any text messages that are important to you you will need to send them to yourself via email.If a factory data reset does not work and it is still doing what it is doing you will need to call your provider or ins. company for a replacement device.

Hope this works out for you