HOW TO SOLVED ISSUE FOR LAPTOP PLUGGED IN BUT NOT CHARGING

The first thing that you need to know is that whether the issue is with the battery or with the operating system. Below listed some of the most plausible reasons and ways to sort out this nagging issue.
There is good way to find out whether the real issue is with the battery or not. You can load an alternative operating system such as Windows or a Linux Live CD. This is suggested because there is no need of the full space capacity and a few hundred Mbs are sufficient. Slax Linux is a great option for this being only around 220MB in size. Again, alternatively you can use a Live Windows repair CD such as the Hiren’s Boot CD or if you have a dual boot system, then you can simply see if the problem persists on the other booting partition.

It has become a common annoyance for some older laptops to suffer battery charging problems. When the issue occurs, with your AC charger plugged in you will notice that the battery is not charging, and hovering over the battery icon in the system tray shows "plugged in, not charging". This can lead to automatic hibernation of the laptop, immediate shutdown at power adapter disconnect, etc.

This issue can be caused by to distinct reasons:

Heating issues - some laptops have built-in heat sensors that will stop charging if the battery, or the laptop itself gets hot. This can be remedied by turning off the laptop for a while to allow it to cool down. It may be worth cleaning the cooling ducts and CPU/GPU heatsinks with compressed air/vacuum.

Battery Driver issues - the default Windows battery device drivers may be corrupt, or incompatible with your particular brand of laptop. If the issue is persistent, it may be worth downloading newer drivers directly from your manufacturer. Below is a solution for resetting the Windows 7 default ACPI battery drivers.
Follow the steps below to fix battery charging driver issues:

1. Disconnect AC power
2. Shut down laptop
3. Remove battery
4. Connect AC power
5. Start laptop
6. Open "Device Manager" (right-click on "Computer" -> Properties -> click "Device Manager" in left pane)
7. Under "Batteries", right-click and uninstall "Microsoft ACPI Compliant Control Method Battery" (all occurances) and, optionally "Microsoft AC Adapter"
8. Shutdown
9. Disconnect AC power, insert battery
10. Connect AC power, start laptop

Notes: If following the above steps does not fix your issue, it may be worth using a voltmeter to verify the voltage coming out of the power supply at the point where it plugs into your laptop. Some power supply cables are prone to failure after repeat bending, and adapters can fail as well. Most common laptop PSUs should output about 19 volts, and there is a label on them that lists the input and output voltages.

The "Microsoft ACPI Control Method Battery Driver" is a Windows service that should be set to start "On Demand" in "Services". The file itself is located in %WinDir%\System32\drivers\CmBatt.sys

If the battery of your laptop is non-removable:
Similarly to the above steps, uninstall the "Device Manager -> Batteries -> Microsoft ACPI-Compliant Control Method Battery Driver" and "Microsoft AC Adapter" (right-click -> uninstall). After that, unplug your AC adapter from both the laptop and the wall socket, shutdown the laptop, and leave both off/unplugged for a minute before restarting.

Keep in mind that if the battery is actually bad, the above may not fix your issue.