No wi-fi on iPod Touch 3rd gen

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My 3rd generation iPod touch was given to me by a friend to fix. The thing thats wrong with it is that the wi-fi button in settings is grayed out and it says "NO WI-FI". I have already tried reseting the device, restoring the device and reseting the network connections. I am now thinking that the wi-fi cable in the iPod itself might be damaged. I was thinking of buying a wi-fi cable for the iPod Touch online and replacing the one in the iPod Touch, I'm not sure if this will fix the problem but i'm hoping it will. Has anyone had this problem before? and if you have did you fix it and how. Also do you think I should try to replace the wi-fi cable? (NOTE: I took the iPod to Apple and they told me it would cost $200.00 USD to fix. I don't want to do that because I might as well buy a new iPod with that money.)