Hello /g/ I need your help, my phone (HTC One mini) got damaged and the power button and circuit underneath are gone, the battery is dead and I have so much files on that phone witch I so dearly belove. The part that is broken is in the pic, its gone. Sorry for asking here but I need help quick
Either take it to a repair company or buy a spare/repair phone from ebay and transplant the component but it's probable that the mainboard was damaged so it's probably fucked beyond reasonably priced recovery.
Hook up a mouse and keyboard using an OTG connector. If you're feeling like doing some real hacking, take one of these, design and 3D print a hinged assembly and turn the thing into a bitching subnotebook.
Is there luck in using tweazers or something similar to activate the power button circuit since this part still sticks out of the phone
That's likely a ground plane connector. Scrape away some of the insulation (very carefully) from the latticed bit of copper and solder some wire between it and the pad indicated here.
Some pics of the actual phone would be useful, along with details of how it happened.