Boot failure: phone quick-flashing on apple logo

Hello,

My sister’s iPhone seems to have developed a fault. It originally started with the phone randomly rebooting under battery power and then getting stuck on the apple logo. Once on the apple logo, it would continuously boot loop and not move past the apple logo. So it’d basically come on with the logo, wait a bit and then reboot.

If I plugged the phone into the mains, it would power up fine and then work. Taking out the charger would force it into a boot loop again (took some time for it to happen, time taken was random though - sometimes it’d do it instantly, other times not). Using PC to power the phone didn’t work. It had to be through the mains.

Now it seems the fault has developed one step further. Under battery power, it refuses to turn on. If I plug the phone into the mains, it will flash on the apple logo.

Here’s a clip of it in action: https://streamable.com/st8aa

Any idea what the problem is likely to be?