Dead New Battery

Question

Bought a Macbook about a month ago, it works fine when its plugged in but the battery won't charge. The green light is on my AC adapter, but my battery % is 0 and the button on the battery compartment shows no lights. Wondering if this is a faulty a battery or something that i did by not unplugging it often enough or "overcharging."

Answer 1

That didn't work, so heres the info you requested:
System Power Settings:
AC Power:
System Sleep Timer (Minutes): 10
Disk Sleep Timer (Minutes): 10
Display Sleep Timer (Minutes): 5
Automatic Restart On Power Loss: No
Wake On AC Change: No
Wake On Clamshell Open: Yes
Wake On LAN: Yes
Display Sleep Uses Dim: Yes
Battery Power:
System Sleep Timer (Minutes): 5
Disk Sleep Timer (Minutes): 10
Display Sleep Timer (Minutes): 1
Automatic Restart On Power Loss: No
Wake On AC Change: No
Wake On Clamshell Open: Yes
Display Sleep Uses Dim: Yes
Reduce Brightness: Yes
Battery Information:
Battery Installed: Yes
First low level warning: No
Full Charge Capacity (mAh): 5083
Remaining Capacity (mAh): 0
Amperage (mA): 0
Voltage (mV): 8419
Cycle Count: 1
AC Charger Information:
Connected: Yes
Charging: No
Hardware Configuration:
UPS Installed: No