I have similar problems with my Compaq laptop (Win XP SP3).
I've never completely fathomed out how they've set it up and the information in the user guide isn't much use either.
The button turns the wifi and the bluetooth on and off, and if it's off none of the other controls work untill it's back on again.
The icon in the notification area (screen bottom right) gives access to a HP Wireless Assistant panel. That allows separate control of the wireless networking and bluetooth, but it can't override the button.
There are a few other ways to control the wireless functions which can be accessed from the control panel and elsewhere. most seem to work at the same level as the Wireless Assistant, but some can switch off the wireless network hardware separately. They foul things up in a less visible way, maximising both the time to restore service and the probability of the computer being flung out of the window.
There doeesn't appear to be any (easily accessible) way of making the machine come on the way I want it to - with wireless networking on and bluetooth off.