Laptop computers run off battery, or DC power. DC means 'Direct Current,' and refers to the way current flows from the source. Direct current is basically a continuous and steady stream of energy. The adapter that came with your laptop computer is known as an AC adapter, which converts the Alternating Current supplied by your wall outlet into the Direct Current that is required to run your laptop. Alternating current does not flow as a steady stream.
A big cause of laptop adapter failures is cord crimps. These can occur when an office chair with casters rolls over the cord on a hard surface. The conductor of the cord can eventually break under the stress of being rolled over. If the cord or insulation is not completely severed, it may not show where the short has occurred. Since most adapters include an LED that will light up when the device is plugged in, a good indicator that there is a short would be an unlit LED.
Any time the adapter has cuts in the insulation of its cord, or is otherwise missing pieces of its insulation, it should be replaced immediately. Bare wires carry a risk of serious or fatal shocks, as well as possible fire hazard. Do not attempt to repair your AC adapter. Contact the laptop's manufacturer or seller to find information about a replacement adapter.
The portion of your adapter that does all the work is colloquially referred to as the 'brick.' The brick is the heavy box that sits between the wall and your computer and is connected by a permanent cord and one that may be removable. The brick, for all its heft, contains some delicate components, and can be damaged fairly easily if it is dropped from a considerable height. Generally speaking, if the brick stops working, the LED that indicates power will not light. If the brick portion of your adapter is not working, you will have to replace the adapter. Contact your computer's manufacturer or the seller for information about a replacement adapter.
The point on your computer to which your adapter connects is not prone to failure, but, being soldered to the motherboard with little other support, can break. If your computer only powers intermittently, or you have to 'wiggle' the adapter to get power, there's a good possibility that the power input on your computer has broken. This is not an easy or quick fix; you may need to replace the entire motherboard, depending on your computer model. A technician should be able to diagnose the problem and give you a price quote on the repair. In some cases, the computer may not be worth the price of the repair.
The easiest way to test your adapter is to plug it in. In addition to the adapter's LED, there should be an additional LED on your computer to indicate that the computer is getting power from the outlet. If neither of these LEDs lights, then there is definitely a power problem. If an identical, 'known good' adapter can be obtained, connect it to your computer. If the computer gets power from the new adapter, then a replacement adapter will fix the problem. If the computer does not get power from either adapter, there is probably an issue with the computer. At this point, it is recommended that the computer be brought to a PC repair technician for diagnosis.
Jury-rigging should never be attempted, due to the risk of shocks, fire and damage to the computer. Do not use another computer's adapter if it is not the same model or brand, even if it fits. Failure to match input and output voltages on laptop adapters could damage the computer, the adapter or both. Contact the manufacturer or the seller of your computer for information about replacement adapters.
If you cannot find a brand and model-specific replacement adapter for your computer, it may be possible to purchase a universal adapter, which includes multiple, interchangeable tips. You will need to find one that matches your original adapter's wattage, and it should also include a matching or switchable voltage output.