I had no sound (input/output), no video, no ability to work on battery. I followed the steps and discovered that both the battery and the i/o board where not properly connected. So following this manual fixed it all. Many thanks!
Thank you very much. I had some trouble with the home button (not reassembled properly), but on the second trial, it worked as described.
Not related to the tutorial, but to the phone itself: I did have problems with the Pentalobe screws at the bottom of the phone (step 1) - I was not able to unscrew one of them, I had to “force” the screen out of the case with one of the screw still in place. It worked.
Took me less than 10 minutes to complete. Computer rebooted as soon as put the MagSafe connector. I had to force a synchronization of the date/hour in Preferences to get it up-to-date (I guess the system would have done automatically a little bit later).
Essentially, you have to follow a very precise order: 1/shut down the computer, 2/take off the magsafe connector, 3/remove the old battery, 4/put back the magsafe connector, 5/put the new battery, 6/power on, each time leaving a few seconds in between.
I just replaced the battery as indicated (with a iFixit part), but the computer says there is no battery connected, even after letting the power plug in for more than one hour.