It sounds like there might be a short. Try with a non-amazon charging cable to see if it's just the charger, you can probably get one at Best Buy, Micro Center, or stores like that. If it doesn't work, I'd recomend just getting a new machine and see if you can salvage the RAM, CPU, GPU, and/or hard drive as some of those may still work and can be repurposed in building your own computer (if you want, it's not as hard as you'd think), or sell them (if going this route please bring them to a repair shop to determine if any are dead. Also if you had anything really important saved to your hard drive you can usually get your data recovered.) Unless you need or prefer a latop, I'd recommend a desktop instead. They're usually easier to deal with when things happen unexpectedly.
TLDR: It might just be the charging cord. Otherwise you're computer's probably toast. Don't buy tech things on Amazon, they often don't work.