Sequence of Actions
First. Make sure that the battery of your iPhone is charging. Put it on charge. First through a PC. If that doesn't work, use an adapter with a plug for a regular wall outlet. It's possible that the phone's battery is drained to zero and there isn't enough power to even open the home screen.
Second. "Hard reset" or "forced reset". The method is a universal remedy for various failures and hang-ups of the phone. Not absolute, but the most effective.
For owners of older models. Within ten seconds, hold down the power and "Home" buttons simultaneously. On iPhone - volume down button instead of "Home".
iPhone doesn't turn on? 5 steps to fix it
Is your iPhone not turning on? 5 steps to fix it
To new users. First, press and immediately release the volume up button. Then do the same with the volume down button. Press the side (power) button. Hold it down until the company logo appears on the screen.
Third. Connect your phone to your PC. Open iTunes. If the software recognizes the device connected to your computer - restore the firmware of your smartphone.
Fourth. Charging did not go? Or it went, but the device was not recognized by the computer? Does not always mean that the phone is out of order. Sometimes it's just the cable. Use another one, but only the right one - compatible with your iPhone model and known to be in good working order. Use it to restore the device's firmware.
The easiest, but not the most obvious option - replace the cable
Fifth. It is possible that the cause is a computer. If possible, put iTunes on another PC. If the computer saw the phone, restore the firmware.