So, I have a mid-2011 Mac mini (2.5 GHz Core i5, dual-core) that has been sitting on a shelf for a while. A couple of years ago, it went belly up. I sent it into a place that repairs logic boards, and received it back, fully functional. After about a month, it went belly up again. Sent it back in, and they fixed it again (warranty repair). Then, 3 months later it died again...and so I threw it on the shelf.
Fast forward to today. Read a random thread where someone referenced heating up a logic board in the oven. Considering the fact that the repair company simply did some re-soldering, I figured why not give the oven and try and let all that solder re-flow a bit.
7 minutes in a 350 degree oven. The Mac mini is now ALIVE!! (I'm currently installing Sierra on it)
Hilarious!