Electronic – How to build a sequential logic circuit with transistors on a breadboard

I'm helping out a student with his homework, which includes building logic gates with transistors on a breadboard, and so far I've successfully built NOT, NOR, NAND, and NOR/NAND logic circuits.

However, the last question is to build this sequential logic circuit on a breadboard, and so far nothing is happening (the LED doesn't light up):

^{simulate this circuit – Schematic created using CircuitLab}

For the above schematic, Node 1 and Node 2 are inputs (either 0 or 1 depending on whether a switch button is pressed) and Node 3 is the output, which is an LED (so presumably it should light up on some kind of combination of inputs).

My NOR gate (which works correctly) is wired up like this:

transistor 1 left: gnd

transistor 1 middle: switch > 10k resistor > 5v

transistor 1 right: connected to the right of transistor 2; connected to 1K resistor then 5V; connected to LED then gnd

transistor 2 left: gnd

transistor 2 middle: switch > 10k resistor > 5v

transistor 2 right: connected to the right of transistor 1

I then made two NOR gates which I need to modify to make the sequential logic diagram above. Right now I have it wired like this, but it's NOT working:

NOR gate 1:

transistor 1 left: gnd

transistor 1 middle: switch > 10k resistor > 5v

transistor 1 right: connected to the right of transistor 2; connected to 1K resistor then 5V; connected to LED then gnd; connected to NOR gate 2 transistor 2 in the middle

transistor 2 left: gnd

transistor 2 middle: connected to NOR gate 2, transistor 1 right

transistor 2 right: connected to the right of transistor 1

NOR gate 2:

transistor 1 left: gnd

transistor 1 middle: switch > 10k resistor > 5v

transistor 1 right: connected to the right of transistor 2; connected to 1K resistor then 5V; connected to NOR gate 1 transistor 2 in the middle

transistor 2 left: gnd

transistor 2 middle: connected to NOR gate 1, transistor 1 right

transistor 2 right: connected to the right of transistor 1

If none of my description makes any sense, can someone just tell me what the expected output for the LED should be? I have two switches, so I can put in 00, 01, 10, and 11 as inputs. What should happen to the LED in those cases?

Edit: Here's my best attempt at a schematic for the sequential logic circuit. Transistors may be flipped around, not sure, but the sides I picked should be consistent (I know which side is which on my breadboard.)

^{simulate this circuit}

^{simulate this circuit}

Tidy-up of schematic edited in by @transistor. I have assumed transistors C and E were reversed in each case.