MacBook 13.3" Battery Not Charging (Dim Green Light)

My macbook is the 2010 model and lately it seems that there has been a problem concerning the battery.
I realized its the battery and not the charger since I tested the charger that I used on other computers and they worked just fine.
I also used other chargers on my computer which ended up not working on my computer but they had still worked on other computers.

Right now, when I normally plug in my charger to my magsafe port, instead of the bright green light that I'm used to seeing, it registers a very faint green light.
On my computer it stated that the charger was plugged in but that the battery wasn't charging. After plugging a charger into another computer and back into my macbook, I am able to acquire the normal bright green light. However, the battery still remains unchargeable. Sometimes, however rarely, when my computer completely dies and plug my charger back into the magsafe port, It'll recharge after a day. The battery indicator would state that the battery was charging when I reopen my macbook. However, after taking out the charger for a few seconds and placing it back into the magsafe port, I am always greeted with the indicator showing that the macbook is unable to charge. I have already tried resetting the SMC and PRAM but nothing has worked. I also realize that it is indicated that the battery should be replaced soon, but is there anyway to fix this problem without having to buy a new battery? Also, I'm running Mountain Lion. You have my gratitude in advance.

Hardware Overview:

Model Name: MacBook

Model Identifier: MacBook7,1

Processor Name: Intel Core 2 Duo

Processor Speed: 2.4 GHz

Number of Processors: 1

Total Number of Cores: 2

L2 Cache: 3 MB

Memory: 8 GB

Bus Speed: 1.07 GHz

Boot ROM Version: MB71.0039.B0E

SMC Version (system): 1.60f6

Serial Number (system): W802222RF5X

Hardware UUID: 913C622B-E577-5C9B-95C0-3B97D6F2C94B

Sudden Motion Sensor:

State: Enabled

Battery Information:

Model Information:

Serial Number: W0021UKJCE1KB

Manufacturer: SMP

Device Name: bq20z451

Pack Lot Code: 0

PCB Lot Code: 0

Firmware Version: 201

Hardware Revision: 000a

Cell Revision: 164

Charge Information:

Charge Remaining (mAh): 556

Fully Charged: No

Charging: No

Full Charge Capacity (mAh): 3617

Health Information:

Cycle Count: 1228

Condition: Replace Soon

Battery Installed: Yes

Amperage (mA): 0

Voltage (mV): 11164

System Power Settings:

AC Power:

System Sleep Timer (Minutes): 10

Disk Sleep Timer (Minutes): 10

Display Sleep Timer (Minutes): 10

Wake on AC Change: No

Wake on Clamshell Open: Yes

Wake on LAN: Yes

Current Power Source: Yes

Display Sleep Uses Dim: Yes

PrioritizeNetworkReachabilityOverSleep: 0

Battery Power:

System Sleep Timer (Minutes): 10

Disk Sleep Timer (Minutes): 10

Display Sleep Timer (Minutes): 10

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: 0x0000

Revision: 0x0000

Family: 0x0000

Serial Number: 0x00000000

Charging: No