The button doesn't directly turn on the wifi. There is some "helper application" that HP installs to respond to the button and turn it on.
You see this a lot after folk use a registry cleaner.
In closing I can't be any more specific since I can't fine the model number.
I can't turn on wireless on my HP laptop (button fell off). Can't turn it on with FnF8 or in devices, or in networking. Is there some other place I can turn wireless on? Everything else is working fine on my computer, but it's toast if I can't get Internet.