Sounds to me like the hardware has failed. Let me guess, you dropped it and now it doesn't work? No. Let me have another guess, you dropped it in a puddle of water, and now it doesn't work? No. Oh, let me guess, you gave it to your child, who handed it back to you not working?
If mechanical buttons work, but the screen doesn't it sounds to me like the digitizer has been broken, and you need a new phone!
An useful tip to fix the issue is to knock the touch screen. It sounds like a child's play but this means is tested by many users already. So you can try to knock on every corner of the touch screen gently for a few times. This would help to connect the digitizer cable to the device tightly.
If the touch screen of your phone cannot work without experiencing any physical damage, it is probably caused by software issues. In this case, there are several means you can try to fix the issue.
Restart the device
When an error occurs on your phone, the most direct but simplest way to settle the problem is restarting the device. That's because this means can stop all the running applications on your phone which can release the device from heavy load. And the operation is very easy- press down the Power button until the screen gets dark. Then wait a minute and hold down the Power button once again to start the phone.This way can turn your phone back to normal status at most time.
Take out SD card & SIM card
Sometimes the SD card or SIM card on your phone would cause some issues as well. Thus, you can try to:Turn off the mobile phone and then remove the back cover of the device to take out the memory and SIM card.
After that, you can reboot the device and check if the screen is responsive now.