"I don't think it will make a difference if you have the sticker or not but I couldn't say that for sure.
The only other thing I can suggest if you have tried everything else is to see if you have tightened the screw as in the first suggestion and to replace the wifi emi shield.
I messed about with my iPhone yesterday with the bottom speaker part to see if it had any effect on the wifi and it would appear that it is actually just related to the antenna and not the wifi as I first suggested. This is really weird as this fix has always worked for me in the past but I guess I must have just been lucky.
If it still doesn't work then it may be that there is a fault with the wifi chip or you may have a blown capacitor?
I've also heard that if you clear the cache, cookies etc on the phone (under settings) then this sometimes helps but I've not tried that myself so don't know if this will make a difference or not.
Anyway, at this point it would be a good idea to change the wifi emi shield to see if that helps (I've included a photo for you so you know which part it is). If it still doesn't work after that then I would say that the board has a fault."
"""I do know which parts are wifi related as it's the parts that I told you about already (I fix iPhones for a living so I know what I'm talking about).""
Clems you do realise the first picture that you posted is of an iPhone 4 battery connector not the 4s don't you?"
Check to see if you accidentally pryed up the soldered connection, these are the usual symptoms. you can actually press it back into place without resoldering and wifi will work ONLY when you're next to the router,
