I would recommend trying to replace your battery first. Your battery may not be storing enough charge to fully boot the phone. This could be caused from a failing battery. It may have enough power to turn on the device but not enough to boot into the operating system. From my experience the battery needs to be at around 3.4v to boot into the operating system. I am leaning toward a faulty battery because it shuts off after booting into recovery also. So me guess is the battery does not supply enough power to the phone. Usually if your battery is healthy but has a low charge you can plug it into a charger and get it to turn on and boot into the operating system. Now if you have a faulty battery it likely will not boot up. If you have been having any issue with charging the battery or it being recognized by your PC you may want to try cleaning your charge port out first to remove any build up. You may also want to make sure your power button is moving freely and is not getting stuck. There are many things that can cause boot loop. Some of the most common are failing batteries or power issues, failed updates or flashing/software issues, stuck power buttons just to name a few. Hope this help some.