Hi Carlo,
You were noting that The power button is only for turning the computer on or quickly going to a menu that gives the choices of either "shuts down","sleep", or "restart." That's what I thought too, but the tiny white "manual" that Apple provided with my iMac lists: Press the power button on the back of your iMac as one of the ways to wake it from sleep. I put the computer to sleep manually by using the dropdown menu under the Apple icon, then pressed the power button. I was afraid it might turn my computer off or restart it, but it just woke it up (right where it was when I put it to sleep) and it connected to my wifi within about 20 seconds.
I know your earlier fix is marked as the correct response, so it's obviously a good one. For myself, I don't have Time Capsule (I just use an external drive for the backups and have an AT&T router/modem). You obviously know what you're doing, but I'm a nervous wreck when I'm doing anything remotely technical with my computer, so the power-button wakeup is a nice easy workaround for me until Apple gets this problem fixed. (Although it is hard to remember to wake it up that way; I'm so used to using the mouse or the keyboard.)
Your original fix is probably better and more permanent, but this workaround does get my computer connected to wifi everytime (so far, at least).