Chosen Solution
I followed this guide and loosened the logic board with a bent coat hanger (it was really hard to loosen it). After reassembly the Mac Mini doesn’t start at all. I wonder if I’ve damaged the logic board? I’ve disassembled it once more and tested the new SSD in another computer, it works, and reassembled it again, still doesn’t start. I’ve attached a photo of the logic board.
I would double check the power connector. From the picture of a small part of the logic board I don’t see anything that I would think would stop normal operation.