Hi!
I've just had the exact same problem as Dirk had, on my MBP 15 Mid 2009 and its genuine battery: no charge, magsafe LED always green, battery stuck @ 40% & MBP would only start with the power cord connected. It would shut down instantly when removing Magsafe.
Coconut battery was pretty confident regarding the good condition of my battery, but still it wasn't operational at all!
I've tried all the resets you could imagine (SMC, PRAM & NVRAM & so on...) and all the fingers/keyboard combinations the guys at Apple came up with, without any success!
I finally found this post.
All my little "mac world" was about to collapse when I read Dan's answer > Logic board problem (no offense Dan) - but I kept reading. Hope came back when I read Andreas' contribution.
I couldn't swap battery like Andreas did, but I tried to remove it from the mac (without any pentalobe screwdrivers - that's a challenge).
I started the mac on power supply without no battery fitted: booted up fine.
I finally reinstalled the battery in the MBP and powered it without any power supply: AND IT WORKED !
It looks like the battery needed a "hard reset" SMC couldn't offer.
Anyway, I hope this trick will help some of you.
This message is not aiming at trying to determine who's right and who's wrong, I only want to share my experience.
Big kiss from Paris.
Patrick.