Interesting problem.
Have you swapped the cpu fan? since I missed which mobo, most new ones will shutdown almost immediately if they don;t detect the speed signal from the cpu fan. move the pcu fan to another plug, plug any 3 wire fan to the cpu position and try powering up. if it powers, go to bios, pc health or monitoring whatever they call it, and see if there is a cpu speed sense shutdown option.
Also you mentioned it came to life wen you loosened the hsf. this brings 2 other possibilities:
1. the mounting is flexing the mobo and has possibly caused a minute crack in the patters that opens on occasion.
2. the cpu is not properly seated, which can cause the same scenario.
Ditto for the nothbridge hsf.
Just a couple of thoughts that haven't popped up before.