Half H-Bridge using IR2104 doesn't work
Do you understand how the IR2104's bootstrap diode and capacitor are supposed to work?
C1 is intended to be charged up to 12V and then floated up to be between Q1's gate and source so a 12V source-referenced voltage is available to turn on Q1.
The diode prevents the C1's charge from dumping back into the supply when it is floated up and it's negative terminal is at a voltage higher than GND.
But C1 has to be charged from somewhere, and it has to be charged periodically. Are you aware that Q2 has to turn on frequently and periodically in order to refresh the charge on C1? Only when Q2 conducts does current flow from 12V to GND through D1 and C1 to GND in order to charge up C1.
At startup, Q2 must be turned on before Q1 in order to pre-charge C1. Then during operation Q2 has to periodically turn on to continue to refresh C1 so that Q1 can turn on. Usually Q2 turns on frequently enough during regular operation (like commutating a motor, switching an inverter, or synchronous rectification) of the half-bridge that no special switching of Q2 needs to be done.