The best one would be if you have Voltage at the AC Adapter but little to no current so that means that the Battery is not charging and has run down below the threshold of being able to power on the system. The easy way to test that is to try the AC Adapter on another NB and see if it charges the battery.
If it's not that then there has to be a failure on the M'Board of the Note Book and that effectively means that you have to look for another NB as most times it's cheaper for the owner to buy a new system than to pay for a replacement M'Board and Labor in fitting it.
A couple of possibilities here
The best one would be if you have Voltage at the AC Adapter but little to no current so that means that the Battery is not charging and has run down below the threshold of being able to power on the system. The easy way to test that is to try the AC Adapter on another NB and see if it charges the battery.
If it's not that then there has to be a failure on the M'Board of the Note Book and that effectively means that you have to look for another NB as most times it's cheaper for the owner to buy a new system than to pay for a replacement M'Board and Labor in fitting it.
Col