The laptop battery is a finicky thing. OEM ones (originally equipped with the laptop) generally tend to be reliable, but they will start behaving in less desirable ways if left to sit for very long periods without use. They are designed to be used frequently. You can shelve them for a while, but it's a good idea not to do it with them near depletion (I've heard it generally recommended to be around 75% charged, and kept in a cool dry place). Once a battery has been strained, it can start behaving oddly like working fine for a while but then rapidly losing charge all of a sudden.
It's generally not a good idea to try repairing a laptop adapter wire, unless you're skilled in this kind of thing. It could very well be that your repair may power the laptop but not handle charging the battery simultaneously. In any case, what you should do is try to calibrate the battery. If you're not sure how to do this, here's an outline:
Laptop Battery Calibration for Windows Vista/7
1. Create Start > Control Panel and double click Power Options
2. Click Create a power plan on the left side of window
3. Select the Power Saver radio button
4. In the Plan Name field, type the name you want to call the power plan, i.e. Battery Calibration
5. Click the [Next] button.
6. Click the [Create] button.
[NOTE: At this point your new power plan is active and you can choose to change other settings in the plan, (i.e. "Put the computer to sleep" to "Never"), from the Select a power plan window that is active or just close the window and continue.]
7. Change the Critical battery action to Do Nothing by clicking Start > Run or Windows Key+R and
type powercfg -setdcvalueindex scheme_current sub_battery batactioncrit 0
8. Click on the [OK] button, and make note of the time (this will give you a base-line to know how long your battery lasts from full to exhausted with continuous use).
9. Use the laptop as normal and stop any work before the battery runs out.
[NOTE: Remember to change back to your normal power scheme once you boot the laptop.]
10. After the laptop battery is completely discharged, reconnect your power supply and turn on the laptop.
11. Once the laptop boots, login and restore your previous Battery critical action by using Control Panel > Power Options and change you plan settings for your current power scheme back to the way you had it, or use the same command in step 7 as follows:
Use the following command for Setting you critical battery action to Sleep
powercfg -setdcvalueindex scheme_current sub_battery batactioncrit 1
Use the following command for Setting you critical battery action to Hibernate
powercfg -setdcvalueindex scheme_current sub_battery batactioncrit 2
Use the following command for Setting you critical battery action to Shut down
powercfg -setdcvalueindex scheme_current sub_battery batactioncrit 3
CAUTION: This setting is only for running the battery completely down. It may cause loss of data and you need to make sure you are not edit/saving data when the battery runs down and the system turns off. This setting will not allow the computer to shutdown, hibernate or sleep. It will just turn off.
It's a good idea to run the battery calibration at least every 3-4 months, if you leave your laptop plugged in most of the time. Otherwise, at least every 6 months. Laptop batteries tend to start losing their charge holding capability after one year, and usually wear out after 2-3 years with regular use. Lithium-ion batteries do have a limited shelf life as well, and storing them after they've been put to use won't extend their lifespan very much.
