This is as far as I got. The top screw won’t come out. The bottom screw came out fine. Oh well, time to put everything back together again.
Before anyone starts tearing down their Thunderbolt Display to replace the Thunderbolt cable with a new one (like I did): a much easier alternative is to plug a standard Thunderbolt cable into the Thunderbolt port at the back of the display. Apparently it’ll work just fine. The only catch is if you happen to need that port for something else.
Pentalobe is only for the screws on the bottom cover. The Torx screw driver is for the remainder.
Thanks to this guide I saved my broken MacBook Pro from a coffee spill that killed the battery. It cost me about 30% compared to what it would have cost to have the battery changed at an Apple authorized repair center. It wasn't easy to do, but that just made it all the more satisfying.
One comment: the new battery pack I bought came attached to a thin film which had to be removed. I unfortunately tore off some of the strips of glue attached to the back of the battery cells, before getting the hang of it. No big deal. But if you have to do the same thing: peel slowly.
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