My iphone 4 dock connector stopped accepting charges with the message "This accessory may not be supported". And that was with Apple cables and chargers. All attempts to clean the dock connector yielded no results.
It was fairly straight forward, just keep a paper, pen, and tape handy to identify and secure screws at each step.
I had to redo the procedure because my home button didn't work the first time. You really could use a magnifying glass for this process. I managed to seat the home button cable properly the 2nd time, then everything worked.
iPhone 5 Liberation Kit
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iPhone 4 (GSM/AT&T) Dock Connector