Battery not charging while still using power adaptor

My battery for macbook air 2012 does not charging anymore while it still use power from power adaptor normally. (the light on adaptor does not light up either)

I just have a new battery from the recent repair under protection plan from Apple. Anyone can help?

Battery Information:

Model Information:

Serial Number: D86518400RWDKRNAX

Manufacturer: SMP

Device Name: bq20z451

Pack Lot Code: 0

PCB Lot Code: 0

Firmware Version: 406

Hardware Revision: 000a

Cell Revision: 162

Charge Information:

Charge Remaining (mAh): 0

Fully Charged: No

Charging: No

Full Charge Capacity (mAh): 6669

Health Information:

Cycle Count: 1

Condition: Normal

Battery Installed: Yes

Amperage (mA): 0

Voltage (mV): 7093

System Power Settings:

AC Power:

System Sleep Timer (Minutes): 0

Disk Sleep Timer (Minutes): 10

Display Sleep Timer (Minutes): 10

Wake on AC Change: No

Wake on Clamshell Open: Yes

Wake on LAN: Yes

AutoPowerOff Delay: 14400

AutoPowerOff Enabled: 1

Current Power Source: Yes

DarkWakeBackgroundTasks: 1

Display Sleep Uses Dim: Yes

Hibernate Mode: 3

PrioritizeNetworkReachabilityOverSleep: 0

Standby Delay: 4200

Standby Enabled: 1

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

AutoPowerOff Delay: 14400

AutoPowerOff Enabled: 1

DarkWakeBackgroundTasks: 0

Display Sleep Uses Dim: Yes

Hibernate Mode: 3

Reduce Brightness: Yes

Standby Delay: 4200

Standby Enabled: 1

Hardware Configuration:

UPS Installed: No

AC Charger Information:

Connected: Yes

ID: 0x0000

Revision: 0x0000

Family: 0x0000

Serial Number: 0x00000000

Charging: No