I'm sorry to resurrect an old thread, but I'm having the same problem here. At least 10 Google searches and 5 forum searches brought me here. Two different working batteries tested. Resetting the SMC didn't help either.
TL;DR: Battery causes macbook to go to sleep, no matter what.
Here's the exact circumstances:
If the battery and A/C adapter are plugged in, the computer will start and show the gray background for about 1/4 of a second then go blank. Not dim, just blank. Pressing the power button again will turn it off immediately.
If I wait at least a minute before pressing the power button, the screen lights up for another 1/4 second showing a blue background and nothing else then goes to sleep.
Bringing it back from sleep gives the same result. 1/4 second blue background then blank.
One time when resuming from sleep I did see the login screen.
If the A/C adapter is plugged in and the battery is removed, it starts up fine.
If the battery is installed while it is on, the screen goes blank almost immediately and the laptop power light indicates that it has gone to sleep after a couple seconds.
Pressing the power button again to resume from sleep did bring up the screen again for about 1 second this time. After it comes up, it goes back to sleep.
Pulling the A/C adapter at any time while the battery is in will power off the laptop indicating the laptop isn't getting any power from the battery.
When initially plugged in, the light on the magnetic plug is red, but after a minute or two it turns green.