MacBook Shuts Off Abruptly

A few weeks ago, my macbook started shutting down abruptly whenever it was unplugged from the charger. The battery says it's fully charged, with full green indicator lights on the actual battery. The macbook will work fine as long as it stays plugged in.

I have heard all different things: power board; logic board; battery problems. Which is it? Hoping to get some insight without having to take it into the Genius Bar.

Here is my battery info:


Battery Information:

Model Information:
Device name:
Pack Lot Code: 0002
PCB Lot Code: 0000
Firmware Version: 102a
Hardware Revision: 0500
Cell Revision: 0102
Charge Information:
Charge remaining (mAh): 0
Fully charged: Yes
Charging: No
Full charge capacity (mAh): 0
Health Information:
Cycle count: 0
Battery Installed: No
Amperage (mA): 0
Voltage (mV): 0

System Power Settings:

AC Power:
System Sleep Timer (Minutes): 10
Disk Sleep Timer (Minutes): 10
Display Sleep Timer (Minutes): 10
Automatic Restart On Power Loss: No
Wake On AC Change: No
Wake On Clamshell Open: Yes
Wake On LAN: No
Current Power Source: Yes
Display Sleep Uses Dim: Yes
Battery Power:
System Sleep Timer (Minutes): 10
Disk Sleep Timer (Minutes): 10
Display Sleep Timer (Minutes): 2
Wake On AC Change: No
Wake On Clamshell Open: Yes
Display Sleep Uses Dim: Yes
Reduce Brightness: Yes

Hardware Configuration:

UPS Installed: No

AC Charger Information:

Connected: Yes
ID: 0x0100
Wattage (W): 60
Revision: 0x0000
Family: 0x00ba
Serial Number:
Charging: No