I want to make the LED turn on only when it receives 0V after a timed 5V input
What you have asked for is impossible. Because you said that you need to turn off the LED at the rising edge of the input pulse (when the pulse width is less than T).  

First, you have to measure the pulse width. Then you have to decide what to do. So you can't change the state of LED before measuring the width.  

If you want to turn off the LED after the input pulse is provided, then it is possible.  

The easiest approach for you will be to use an Arduino. In your code start a counter at the rising edge of your input pulse and if the counter value exceeds a specific range then turn on the LED and stop the counter. And if the falling edge comes before your desired limit, then turn off the LED.  

And if you want to go in a hard way then take a capacitor and a resistor. Charge the capacitor through your input pulse. With time the voltage across the capacitor will increase. Use analogue comparators to find out when the voltage reaches the desired level. But you will need an oscilloscope and the process will be tough. You will need a D-Flip flop to hold a state.