What's the background on this device? Was it dropped or exposed to water. Perhaps a screen was replaced recently...any info helps us understand how this problem may have started.
Boot-looping devices are hard to troubleshoot. It could be hardware or software although in this case it is leaning towards hardware. Can you plug it into a USB ammeter to see if there is any current flow while charging?
I would open up the phone and do a good visual inspection (preferably with magnification) to see if anything is out of place, if you find evidence of water or other debris or if there is any visible damage to connectors or flexes.
Then I would disconnect all of the connectors except the battery, Dock and screen (LCD & Digitizer, do not connect the FCAM & Sensor). There are guides here. Plug in your phone and then check to see if the phone is more stable. If it is not, then you may have a defective screen, Dock or a Logic Board issue. If you want, you could try a new or known-good screen and Dock to eliminate the last variable.
If the bare-bones approach works, then add one flex at a time until the problem reappears and replace the defective component. I would start with the Rear Camera, Volume & Power Button, Front Camera and Sensors.