Try the following to determine if the problem is with the adapter or the laptop.
1. If you can or you know someone who can, test the adapter with a DMM (Digital MultiMeter - Voltmeter function) to prove that the adapter is working properly. The meter should read 19VDC.
2. If you do not have a DMM (or do not know someone who does) have you got access to another suitable/compatible power adapter that you can try, to prove whether yours is OK or not? (the output specifications are printed on the adapter- ensure that it has the correct DC plug)
If the meter does not read the correct output voltage the adapter is faulty and needs to be replaced.
If the meter reads the correct output voltage:
Firmly hold the adapter plug into the laptop's power port and gently flex the cable at the back of the plug. Does the charge light on the laptop go on and off with the flexing or remain steady or just goes on then stays off?
1. If the light goes on and off it is either the adapter plug/cable that is faulty or the laptop's power port. This might depend on how firmly you are holding the plug. The idea is to try and not have the power port moving at all.
2. If flexing the cable makes no difference to the behaviour of the charging light, it may be that the DC power port in the laptop is faulty or that the charging circuit in the laptop is faulty. In any event the laptop will have to be opened for further examination. Fortunately, your laptop has the power port as a plug-in part so if that turns out to be the problem it will be easy to fix. Here is a link that shows what it looks like.