May not apply to your situation but my camera was dropped:
I just took my Instax Mini 9 apart (not sure if 8 is the same). The button on the outside of the camera that turns it on basically pushes a black piece of plastic against a spring and triggers a silver piece that looks like a small wrench. That "small wrench" is what triggers the lens to pop out. Sorry, very non-technical. I have no clue what the actual part names are. Anyway, the black piece of plastic had broken and was no longer triggering the wrench piece, therefore not popping the lens out and not turning the camera on. I hit a dead end on getting a replacement part, so I used super glue, put everything back together and it's working great.