battery not charging, green light on (works only with) power adaptor

MacBook pro shut down suddenly while on battery, could not (re)start. I tried SMC but no results. The macbook will not work on battery, as soon as I take the adaptor it shuts down.

I send a coconutBattery reading and these are the specs:

Battery Information:

Model Information:

Manufacturer: Sony

Device name: ASMB014

Pack Lot Code: 0000

PCB Lot Code: 0000

Firmware Version: a41b

Hardware Revision: 0000

Cell Revision: 0000

Charge Information:

Charge remaining (mAh): 3593

Fully charged: No

Charging: No

Full charge capacity (mAh): 5188

Health Information:

Cycle count: 652

Condition: Normal

Battery Installed: Yes

Amperage (mA): 0

Voltage (mV): 11757

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): 85

Revision: 0x0000

Family: 0x00ba

Serial Number: 0x00559f4b

Charging: No

Will be grateful for any advice,

Carlos