How to build a sequential logic circuit with transistors on a breadboard
Assuming the redrawn schematic is an accurate representation of what you actually built, then the problem is that you have the LED connected directly in parallel with the B-E junction of Q2.

The circuit is working, but Q2 prevents the voltage across the LED from rising high enough to light it up.

The fix would be to make the connection between the base of Q2 and the LED using another 10 k&Omega; resistor. This will limit the current into Q2's base and allow the LED to light up.