You said "considering i did it right", not sure how you did it but I strongly suggest to follow TurTLeG lead and perform the second step, which is to check the integrity of the voltage the fan is receiving via its dedicated terminals, so that you 100% isolate the problem, I would hook up a voltmeter in parallel with the fan terminals, start the car and then shortly start the AC, find out if the fan receives a voltage in due time and how much. If it gets the right voltage in the right time then definitely your fan is out.
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