IR LED won't turn on, but white LED will in IR repeater circuit
It does not work because it is the wrong component for the circuit, or wrong circuit for the component.
The TL1838 is a IR receiver module that demodulates the 38 kHz carrier away and leaves you the signal without 38 kHz carrier.
So either re-encode the 38 kHz carrier before sending it to the IR LED, or get a module that does not demodulate the signal.