Mine also stopped holding a charge after about three years. I found a high quality (?) replacement on Amazon Prime for $10. Definitely easier than trying to replace the battery.
Great instructions. iFixit's associated video is great to watch, but misses a few steps (like step 13, the little triangular thingie). These instructions were much better. I used the small screwdriver previously purchased from iFixit, magnetized it (which REALLY helped get the screws back in), took lots of photos as I disassembled it, and used numerous small jars with stickie notes to keep each set of screws separate. I also used a lighted table magnifier (like old people use for reading). My new cable works great, thank you once again!
That was INCREDIBLY easy to do, thanks to both your instructions and people's comments. 10-15 minutes, start to finish. Tweezers and a good set of bifocals helped too :-)