all those answers are rubbish,
this answer from elva carri on ifixit is much better,
I had the same issue. Tried everything here bar the teepee suggestion which i was intrigued by but went for a free diagnosis at a repairs shop before trying that one.
In my case it was a broken ram slot so it works with one piece of ram removed.
Regarding the teepee method the guys in this repairs shop have a machine that does the same thing. They call it floating it and i think were impressed at your idea of how you could do this yourself, thought it sounds like in my case it wouldn't have fixed it.
best of luck