The charger is functioning well. There are still two possible reasons why your computer is not turning on. 1. The battery, 2. The computer itself.
What you need to do is to isolate the problem.
Here's what you can do to isolate the problem.
1. Remove the battery from the computer.
2. Turn on the computer using the cord. Remember not to put back the battery yet. Just the cable and the computer connected. If the computer turns on, then, you need to replace the battery.
3. If it still not turning on by using the cord alone. Try to wiggle the cord to check whether it's loose or not. Check if there are some signs of power on the computer. If there is a power like lights lit in the computer, then, it's the computer that's having the problem. You need to bring it to a technician if that's the situation.
Please let me know if there are any development after doing the troubleshooting above so that I can get back to you if you need my help.