not working nor with battery nor on power cord. Not even the light that it's plugged in is working
That means that the power is not even reaching the BIOS on the motherboard (mobo). If the mobo failed, you at least would get the power light on the wall converter (I assume that is what you meant by "the light" in your post) and the hard drive should spin up but the screen would be dark and unresponsive. Same thing if the CPU failed. If the above is true, then it is possible that the power supply in the lap failed. It is also possible that the adapter failed, although that doesn't happen often. If the battery would no longer charge and the adapter was still good, the lap should boot as long as the wall adapter was plugged in. The battery would still pass power through, but it just could not store power. But if the lamp on the adapter "brick" itself is dark, then that is most likely the problem.
Now, if the "light" you referred to is NOT on the adapter (IOW the adapter has no power-on lamp on it), but is a power lamp on the laptop, then the above would still hold true, with one additional possibility: the jack (on the adapter cable) that you plug into the socket on the lap may be bad and/or the socket in the laptop could be bad. This is very common on laptops. Try to "jiggle" it a bit to see if the power lamp suddenly flashes on and off. If so, you have found your problem. If not, check the jack connetion at the wire junction: if frayed and there is a crack or the wires are visible, it could be broken there. AS far as checking the components (re: power supply), you would have to take it into a shop. OR you could check Youtube for a "howto", most everything is on Youtube now. Just search Youtube with your make and model laptop.
You probably could replace the laptop for what a power supply replacement and labor would cost. In addition, the realtiy check is that new parts for a lap that old are impossible to obtain, you would have to try Ebay or somesuch. Unfortunately, laps are not like desktops, which some components are easily obtained and replaced.
For example, a bottom of the line lap that will work fine for normal usage (not gaming or video editing, etc.).