08-04-2016 04:16 PM
I wanted to post my solution in case it helps anyone.
Fix: I put a piece of tape on the SW2 switch to hold the switch down, removed the battery, removed the CMOS battery and pressed the power button 10 times followed by another press for about 5 seconds. I had already used this sequence of steps (except for the SW2 step) to restart my computer, but it would turn off as soon as I unplugged it. The reason why it kept turning off is because the SW2 switch wasn't being pressed by the bottom cover when I closed the computer. This purpose of this switch is to disconnect the battery when the bottom cover is removed, but this laptop model seems to have issues where the bottom cover doesn't press the switch after a while.
The reason I didn't think it was related to this switch is because my computer happened to stop working while the computer was off. So from my point of view, my computer just wouldn't turn on anymore. I tried messing with this switch after I saw RegisterFault's post here: https://forums.lenovo.com/t5/ThinkPad-S-Series-ThinkPad-Yoga/Re-Thinkpad-S3-Yoga-14-Random-shut-offs....
Here's the images from that post in case the URL doesn't work in the future.