Try something for me. Try taking out the battery on the back, probably has some simple latch to take it out, plug in the charger, then try turning it on. That should directly power the laptop through your charger. If it works, then replace the laptop battery, cheap and easy. You would just look up your laptop’s battery. If it doesn’t, it COULD still be that issue. The charger may not be efficient enough to boot it by itself or other problems. So I would still try getting one. If nothing else works, then its your laptops motherboard in which you could try other things but it could mean the whole system is broke. Just give some more detail after trying that, I'm not implying you can’t fix it! Don’t worry :)
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The fact you said you had a static with the machine and its turns off means it definitely fried or damaged some electronically part that keeps it on. So that would make me personally want to assume its the laptop battery!
Try something for me. Try taking out the battery on the back, probably has some simple latch to take it out, plug in the charger, then try turning it on. That should directly power the laptop through your charger. If it works, then replace the laptop battery, cheap and easy. You would just look up your laptop’s battery. If it doesn’t, it COULD still be that issue. The charger may not be efficient enough to boot it by itself or other problems. So I would still try getting one. If nothing else works, then its your laptops motherboard in which you could try other things but it could mean the whole system is broke. Just give some more detail after trying that, I'm not implying you can’t fix it! Don’t worry :)