Since you replaced the flex cable already, it seems to be ok.
However, I would check on both ends of the flex cable. First, check the soldering pad of the power button on the logic board. Is it ok?
Second, and what seems to be the actual problem, check the power button itself. Sometimes the metal plate inside of it can change its position over the time. Or dust can be in between the button and the contact area of the flex cable (which might not be the case since it's a new flex cable and you might have already cleaned that area). You said it still clicks, but I would check anyways. But before you do that, here is what I would do:
If you have a multimeter, unsolder the flex cable on the logic board and check the circuit of the power button in its 'built in' condition. Do you get a beep of the multimeter when you push the button?