The battery didn't hold a charge and would be dead by mid-day
I was watching the iFixit repair guide and a couple of videos on YouTube. I did not want to remove the display entirely since those tiny connectors are hard to line up and connect. I realize I was taking a chance of damaging one of the ribbon cables but as long as you hold the display up in a 90 degree angle it is fine.
I only replaced the little clasp for the Home Button connector and the two screws and plate for the battery connector. Removing the battery proved a bit more difficult than in the videos, probably because I could only pry it from the sides and not the top, due to leaving the display connected and not being able to fold it over all the way.
The Lithium Ion Polymer battery was a bit like play-doh and I was worried I may damage it and it would catch fire like those Samsung Galaxy Note batteries. The two sticky tape strips below were quite strong and I could not find a tab to pull them out from under the battery. Perhaps that only exists on the iPhone 5.
I am also getting an error message that TouchID could not be enabled. I have not been able to fix that yet. I don't think it is the issue that was all over the news as that only happened when a display was replaced. I did a little checking online and it looks like I need to log out of all iCloud services and log back in.
It is definitely worth doing the fix yourself since it only costs about $30 compared to $79-100 in stores, but you should only do it if you are technically savvy.