What Queen-Evie has suggested is a good start. But there are a couple of other things I would suggest that you check first before you go out and purchase a new power adapter.
The first thing you should determine is if the adapter is putting out the correct voltage. If you look at the adapter you will find the voltage and amperage printed on it. If you look on the label you will see the model, the input voltage, and the output voltage. The voltages will look similar to those below. V = voltage A = amperage
Input Voltage 100-240V @ 50/60Hz 1.2A
Output Voltage +12V @ 3A
You can test the voltage with a voltmeter on the DC scale.
Another thing to check is the power connection where the adapter and the laptop are plugged together. A all too common problem with laptops is the power plug. If you don't see the power LED indicating that it is plugged into the laptop wiggle it to see if the LED comes on.
If you find that the voltage is not correct you will need to replace the adapter. The voltage and amperage are very important. It should be obvious that if the voltage isn't correct the laptop will not work, or will not work properly. The same is true of the amperage, with on difference. The voltage needs to be what is listed for the laptop, but the amperage can be higher than what is suggested, but not lower.
I have shopped online for power adapters for members in the past and found adapters advertised to be for a specific laptop, but didn't have either the proper voltage or amperage. You need to pay attention to this.
One last thing to be aware of, this is the number of cells in the battery. If you have to replace the battery you will want to make sure that the voltage and amperage are correct, but you also will want to purchase a battery with at least the same number of cells. Batteries with more cells will be able to hold a charge longer as long as the battery is in good shape.
I would also suggest that you not take the word of a "sales person" at department store like the one listed in Queen-Evie's link.