I highly recommend trying to use your thumb to push and turn the power button clockwise quite forcefully. I had a very similar issue and found this suggestion on a youtube comment on a foreign language youtube video. I did this multiple (10-20 times) and never noticed a difference in how the alignment of the power button looked but eventually, my trackpad powered back up. Best of luck!
I found a YouTube comment that suggested that one needs to periodically push and forcefully rotate the power button side of the trackpad clockwise. I bought a used one that had initially some battery corrosion but worked, and eventually started to have frequent disconnects and then failed to turn on. I cleaned any of the corrosion out of the battery compartment but it still would not turn on. I tried the method of forcefully rotating the power button clockwise with my finger and after a few attempts to do this, the trackpad started working again and now no longer has repeated disconnects. I found this out only after purchasing two more shattered donor trackpads on eBay to use for parts in case mine was corroded and that caused the failure. I will take those two apart in more detail and see if there is anything to be learned about the power button assembly.