Sometimes when i replace a digitizer, i will accidentally bent one of the home button contacts out of place... check the "metal prongs" coming out of the backside of the lcd/digitizer assembly, they should be straight and be sticking out enough so that they can touch the metal pads on the dock flex cable. Also i like to scrape the metal pads on the dock flex cable a little bit to get a better connection.
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- you can test wether the problem is the dock cable or the home button by bridging the home button pads with a paper clip, while the screen lcd is plugged in you should see the iPhone act as if the home button was pressed if the dock connector/logic board is working fine. home button contact pads should be to the Right of the text "J3".
Sometimes when i replace a digitizer, i will accidentally bent one of the home button contacts out of place... check the "metal prongs" coming out of the backside of the lcd/digitizer assembly, they should be straight and be sticking out enough so that they can touch the metal pads on the dock flex cable. Also i like to scrape the metal pads on the dock flex cable a little bit to get a better connection.