In my MacBook Pro, the screw in step 9 that is farthest away from the CPU is a Philips screw, rather than T5 Torx.

I bought my MacBook Pro in 2016, over a year after it came out, so this might be different depending on when yours was manufactured.

UPDATE: I took apart my iPod again, and after a lot of pushing, checking, and pushing again, I got the battery to fit in. I had to use a piece of foam and some double-sided tape to secure my hard drive instead of the blue rubber pads to make the battery fit in height-wise. This is OK in my situation, because I have replaced the hard drive with a compact flash card, but actual hard drives need the cushioning from the blue pads so they don’t break as easily.

I ordered a replacement battery here on iFixit, and it is slightly larger in size than the original. To make it fit height-wise, you need to take the blue pads off the hard drive, which would make it wobble around. Additionally, the battery is a bit thicker, so it doesn't slide into the case easily, and I don’t want to break anything by forcing it. Anyone else have a similar problem with a battery they ordered on here? I expected better than this from iFixit. My old battery still works, so I will use that for the time being.

So, as soon as you press the menu or center button, it resets? Sounds more like a logic board problem. (Have you tried restoring it in iTunes?)