I did have the same problem.To make the long story short, the problem was graphic chip (known problem with Unibody models from 2011) The good thing is that you do not need to replace the whole board, only graphic chip (cost about $ 85 plus installation).
I don’t agree with statement that 17’’ MacBook Pro won’t boot without battery. I have two 17” and one of them is old Santa Rosa model and I’m using it in my summer house without battery for almost 2 years without any problem, so the booting problem lies somewhere else. My guess is not tight connection with mother board and when you place the battery the connection with motherboard is established. Check the flat connection cable, maybe is damage and replace it.