Got a replacement battery from ifixit a couple days ago to replace the bad one they sent out to me the first time. I put that one in and everything works fine now. I would definitely recommend that if you do this fix and are "sure" you did it right, consider that the battery you got might be a lemon. I thought it would be a matter of powering on=good, DOA=bad, but it's apparently much more than that. The first time I did this fix my wifi stopped working and the second time I couldn't get a cell signal. I figured I'd screwed up the repair, but it was the battery. One other tip I learned doing this process a 4th time--make sure all the ribbon cables are above the logic board before you screw it back down. I had #5 pinned under the board, and thankfully didn't damage it, though a small piece of black plastic was near it when I discovered my mistake (maybe from the SIM tray?). But it didn't seem to affect anything. Phone works great now.
Did this once and afterwards Wifi was greyed out, not available and none of the apps would run; just blink back to the home screen. Doesn't seem to be holding a charge--I let it sit plugged in x 30 minutes, it died as soon as I unplugged it--so can't get it to iTunes to restore from backup. I repeated the entire repair in case I missed something, maybe had a slight alignment problem somewhere etc. It's charging now--we'll see.
Tips I learned: cables #6 and #7 are round snap-on connectors. Line them up carefully, they should "click" in place. Also, the "Do Not Remove" sticker got obliterated in the process of repair; first time through I didn't put anything over the screw at the end--wonder if that caused a problem? Second time through I put a small square of electrical tape over it. lastly, cable #3 is tricky. That white bar flips up like a latch. Slide the cable back in at the end, then flip the latch down to secure it.