Sadly your logic board has failed, you’ll need a new one [https://www.thebookyard.com/product.php?cPath=96_252&products_id=7278|Mac Mini Logic Board, 2.3 GHz i5 - Intel 3000] I would recommend getting this version of board as it will last a lot longer than the [https://www.thebookyard.com/product.php?cPath=96_252&products_id=7281|Mac Mini Logic Board, 2.5 GHz i5 - AMD Radeon 6630M] version.
Here’s the guide you’ll need to follow [guide|6421]