Mac mini not booting up, black screen, fans spinning high rpm

There are two versions of this model Macmini5,1 (2.3 GHz) Macmini5,2 (2.5 or 2.7 GHz)

• The Macmini5,1 models have Intel HD Graphics 3000
• The Macmini5,2 models have both Intel HD Graphics 3000 & AMD Radeon HD 6630M discreet GPU (DG)

Most of the failures are within the AMD GPU’s. You might be able to disable the use of the GPU while not as good as the AMD Radeon GPU its better than nothing.

Otherwise its time for a new logic board! Here’s the guide: Mac mini Mid 2011のロジックボード交換 finding a new board is tricky right now as your only option is used parts and due to COVID parts are hard to get as well. Right now the old board I can find is this one Mac Mini Logic Board - 2.3GHz i5 Intel 3000 graphics