I had the same auto startup loop zero battery problem after 6 months or so of flawless use. The tablet experienced zero battery. Upon plugging in the Asus, the power supply would start up, go to home screen, and display "shutting down" after 2 seconds. As it shut down, it would show a screen of "static noise" like an untuned analog tv. Then, say two minutes or so later, it would repeat without any intervention, and ad infinitum. Battery never goes over zero.
There is a thread here that is also about the same issue.
There is an albeit slightly hard to understand fix offered in the above thread, which started with "plug into pc". I tried to follow steps without plugging into PC, as I could see no particular reason why this would make a difference, without joy. I then plugged into PC USB. Large "battery charging" screen immediately displayed, and I'm currently just letting it charge (if it actually is). Very odd flaw. I imagine as the batteries get a little older, this may become a common experience for many.
I recommend checking the Android Central thread. I'll be replying there with my results.
_ just a quick update here (I did put full process I undertook on the other thread though) to say it all worked out well, and after leaving to charge from pc, the tablet finally started up normally again. Phew...