The laptop power jack is not easy to repair. The easiest way to repair it is to replace it. If there are no spare jacks for replacement, it is possible to repair them. In case there is a broken central pin, I would not recommend joining it by soldering it because it can break again. Usually, we take out a piece of the pin that is soldered on the motherboard and join the central pin to the motherboard with a piece of wire. This is a proven way to fix the problem permanently.
If you want to fix the power jack at home, you will be lucky if there is just bad soldering, and it is possible to simply re-solder the pins again. Usually, broken pins occur when the jack breaks and then falls into pieces. In order to prevent this, be careful moving the laptop around when it is charging because the force applied to the adaptor plug goes to the power jack.
I should mention here that Dell power jacks have not two wires, but three. The third wire is for adaptor type sensing. This makes things complicated because this wire tends to break and the laptop does not charge as it does not know what type of adaptor is connected.
Sometimes, the pin of the jack breaks near the motherboard, or the wire breaks in the adaptor plug. But, the battery can also fail, so with Dell computers, it is better is to be sure and check everything. It is also handy to have a spare battery just to make sure is not a battery fault.
There are a variety of power Jacks or DC Jacks on laptops. Here is a burnt power jack.
Here is another example of a burned power jack on a PackardBell laptop.
If it needs to be replaced, it is easier if you use specific tools. For example, the Hakko 808 de-soldering gun.
This is handy, not only for DC Jacks, but also for anything that is soldered with the through hole method. There are many DC Jack types, and the pin map is almost always different. My recommendation is to use the Hakko and to have the tip at 1.3 mm as some jack pins are thick and it is difficult to de-solder them if the tip is too small. What would make de-soldering easier is to heat the jack pin properly and then press the guns button. From my experience, the pin and the solder gun should be heated up properly for easy removal. Practice is key here.
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