The symptom: Touchpad stopped clicking in.
The troubleshooting: I took the bottom off the Macbook Pro Mid 2010 and removed the battery to figure out why the touchpad wasn't working. Adjusted the click screw underneath the touchpad and put the battery back in. The touchpad wouldn't click. So I removed the battery once more. The touchpad clicked down when the battery was removed. Looked closely at the battery and noticed that it had started buldging. BAD NEWS.
Received the battery quicker than I thought I would. Thanks iFixit for the fast shipping. I had been using the Macbook for a few days without the battery by just plugging it into power when I needed it and setting it up to hibernate when I closed the lid or pushed the power button. I removed the bottom and installed the new battery. Buttoned everything up and sure enough. The touchpad was clicky again. Booted up the Macbook and checked my battery health monitor app that I had installed months ago. The battery had more MAh than the original max MAh for that model Macbook. Causing the battery health to jump up to 106%.
Always use OEM parts for battery replacements. Never misjudge a non-clicky touchpad on an otherwise perfectly working Macbook as just a touchpad issue. Things aren't always as they seem.