Mac mini force restarts

Hi everyone, I rarely post on forums but I've been pushed into a corner now and in need of help. My uncle had this mac mini and it was working perfectly and everything. He had his wife's and kids photos on it. His kids use it to play online games(their like 2-4 grade so they play those random online mini games). Lately it has this HUGE issue. He can't seem to "actually" log on. He is able to get to the log in screen after booting up and put in his password and stuff. He can get to the part where he can see loading bar below his profile picture. After it fills ~1/4 of the way the mac mini shuts off forcibly. He asked me to take a look at it. I've been working on it for the past week or so now and have made 0 progress. I have tried searching and seeing if anyone else had the same problem. I tried solutions that people used for similar problems but to no success. I've found out that whenever I leave the mac mini alone for a couple of minutes it turns off by itself(idk if that's a setting on the mac mini or not. I've also tried to boot in safe mode but it doesn't work(holding down shift during boot up but it goes to its normal log in screen). I've also discovered(i think) that the mac cant find its boot drive? The "? mark in the folder" icon doesn't appear but whenever I try to select boot drive using the startup command keys I have to unlock the drive first before I am able to select it. When I do unlock the drive and restart the mac mini the drive gets re- locked(i guess) and the same initial problem happens. I'm also oddly unable to change my password using the terminal "resetpassword" thing( i still have to unlock the drive to make it pop-up in the volume select screen for this as well). Also unable to cahnge password using the password recovery options. All the hard ware is stock model. He is running 10.10.5 (yosemite i think). Please leave any questions and/or comments below. I really need help fixing this issue. Also if there is anyway of extracting his photos and videos without actually logging in and then hard resetting the mac mini he is fine with that. He really wants his photos cause they are photos of his children when they were little. I thank everyone who took their time to read this. I'm really sorry if this sounds like a rant but I want to give as much info as possible. I may have missed things so please ask questions and i might be able to answer them. I'm not very software talk savvy so please if possible could you keep things in simple terms XP if the only way for you to describe your comment/question is in a software heavy talk than please feel free to leave your comment as you like. I'm willing to go the extra step and learn more software talk if it means fixing this mac mini.