Chun,
you may be able to use a comparator powered by the battery such as the ADCMP350
http://www.analog.com/en/special-linear-functions/comparators/adcmp350/products/product.html
you need to rectify the AC with a diode and capacitor and compare that voltage against the internal reference of the ADCMP350.
The open drain can be used to drive a FET to turn on the LED.
A second comparator can be used to enable/disable the charger. In this case a window comparator like the ADCMP670 or a dual comparator with programmable hysteresis like the ADCMP343 may be useful
http://www.analog.com/en/special-linear-functions/comparators/adcmp670/products/product.html
http://www.analog.com/en/special-linear-functions/comparators/adcmp343/products/product.html
We do not have high voltage battary chargers.
Good luck with your project.
LucaV