hey, feeling with you.
I recently updated my Xperia T to 4.3.
While in 4.1.2 the "low battery" behavior was quite weird, as my T did not charge (no red LED), I was able to get it back to life by pressing and holding the power button for quite some time, lets say 5 min. or so, as it was loading then. This was independent from whether it was exhausted (blinking red LED) or "simply of"(not blinking but not charging anyways).
Through this whole power pressing procedure (I just wrapped the cord around the phone several times) the LED was red and the phone was charging, but it did not turn on. After the 5 min. I freed the T an hit the power button again. Now it was booting as expected and did not immediately go off again.
On 4.3 unfortunately this does not work anymore
. The phone just tries to boot and enters the reboot cycle as you described (with the difference that it does shut down instead of reboot).
Now first I would like to know, if your T behaved like mine under 4.1.2 (guessing that was your last Version too). From what I've read I assume that wasn't really normal behavior. I think there must be something wrong with the hw, as my 4.1.2 was neither unlocked nor modified in any other way.
Second I would advise you boot into recovery and select boot into bootloader* (if you have installed one) or connect your T to your PC and boot into flashmode (power+vol.down I guess) as it might charges in there. The recovery worked for me, flashmode should work, but I never tried.
Finally I guess chances are good, that your device works totally normal if it gets charged again (just don't let it run out of energy again
btw. does the Xperia T normally charge while it's powered off? Anyone has send his phone back on warranty because of charging problems?
good luck to you,
*I am using this 4.3 rom (http://forum.xda-developers.com/show....php?t=2647459
) atm, as I have root there. But the recovery is really buggy right now so it just restarts all the time. I'm not quite sure where the "boot into bootloader" option gets you ( never heard, that you could boot into bootloader on an xperia device) but the LED shines blue and the T charges and that's important right?