Your machine has er... issues :P
Seems to be something lose in the motherboard power connector. I am not sure if it is a lose pin or something more. I stopped messing with it. I now really dislike MB mounted processor fans. It is easier to put on but does not seem to seat worth a durn. No wonder it takes so much grease. I think there is another issue but am not sure what.
Great.... that's par for the course. Don't worry about it too much, I can't use it anytime soon anyway.
I hate the motherboard-mounted fan too, you're right, it's way too loose and it takes a lot of work to seat right.