My MBP 2010 will only power-up if I disconnect power and battery, and then only connect power. When I shut it down, it'll only power up again if I remove the power first for >10 seconds.
I've tried an SMC Reset, a PRAM Reset, but nothing works unless I disconnect everything for >10 seconds.
It seems especially odd as even though it starts up the first time, it won't start up a second time without the complete power disconnect. Note, if i reboot, it restarts fine.
The battery is charging correctly, and I get the appropriate green/orange lights on the MagSafe.
For now I've left the battery disconnected, so at least I can work around this.