Why is my phone not turning on

Your phone is boot-looping. A boot-looping device can be caused by many things. How was your battery doing before this...was it struggling to hold a charge and not lasting very long? If the battery was weak, that would be one of the first things to try replacing. Give us more history by commenting on this answer.

Try these things (if you haven't already) to see if anything helps:

• Try a hard reset (Home & Power button for 10 secs)
• Use a genuine Apple Lightning connector
• Use a genuine Apple charging brick and let it charge overnight
• Try to connect it to different computers (mac/pc if possible) with an updated iTunes
• Put the phone in recovery mode (search DFU Mode). Careful, this can reset your data
• Use 3uTools for putting it in and out of Recovery Mode
• Use 3uTools to flash the firmware (you can't downgrade)
• Check the condition of all the flexes (with magnification)
• Disconnect the Front Camera Ribbon from the logic board and reboot your phone
• Disconnect the screen assembly completely and see if iTunes will recognize the phone.

Otherwise, you may have a logic board issue. If you are uncomfortable doing these steps, consider finding a repair shop to do the troubleshooting. A shop that also does micro-soldering can go deeper if the problem is not modular in nature.