Backfeed gate output to input with OR gate made out of BJT transistors is not working
It is working exactly as it should from looking at your screenshots. When the input is high, the upper BJT is turned on, and current can flow to the LED. 

When the input is low, the lower BJT is pulled down via the 5k resistor so both BJTs are off, and the LED will not illuminate.

So it looks to me like it is working as it should with this configuration. If you want to design an 'ideal' OR gate, you will need more than just 2 BJT transistors and a few resistors. 

For example, just have a look at a TI OR gate (DATASHEET LINK):