Have this issue also -- took my iPhone 6 to an Apple Store and they said it is a hardware/firmware issue and the phone will need the be replaced for $300. My phone was only about 14 months old and barely out of warranty. I made the case that the phone worked just fine until I tried to update to iOS 9, and then it got stuck in the "connect to iTunes" screen -- when I tried to restore, it failed with error 53. Anyway, pretty disappointed in Apple's lack of standing by the quality of their product. Their response was "Well, you should have gotten Apple Care". Bullshit. My phone is barely a year old, never got wet, always protected in a shock-proof case, never handled roughly, and worked fine until this update. A $450+ product should not fail due to a company-pushed update.
Regardless, I am interested in hearing more about the flex cable replacement I have the original touched home button -- is it correct to say that I should be able to replace the flex cable and potentially solve the problem?.