iPhone not booting on battery but works on plugged in?

iPhone 5 it won’t boot, when i switch on apple logo comes for 5 seconds and goes off, and it repeats the same boot 20 times, then it says battery with red bar 1%, and goes off,

but instead when i plug my USB cable to power source/charger it boots successfully, and battery charging as usual 70%, everything works fine, after 100% charged, when i unplug my cable again, problem occurs-boot loader,apple logo 5 seconds, repeats upto 20 times, and battery red bar.

again when i plug charger it works, but when i plug my USB to laptop, it won’t boot,

WHY?

i checked all the hardware’s, checked battery voltage: 4.17v with multi meter. battery is perfect, hardware are no dust or clean,

I updated & restored phone via ITunes, the problem not fixed yet,

Why?

Please Help?

what causing the issue? Battery or Software or Hardware?