Computer Advice/Recommendations

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Lately, my HP Notebook laptop (specs in picture) has been turning off after only 10-15 minutes on battery power, though it works just as well as it always has when plugged in. I ran a battery check test, but it could not detect any issues with the battery. I also checked the computer's advanced power settings, and there is nothing there that looks like it would cause such a problem.

I am inclined to believe that my laptop's battery has actually gone to shit, despite what the computer says; when it does abruptly turn off, it is like what happens when your computer runs out of power, and once it turns off, I cannot turn it back on until I plug in the charger. It's at least some kind of hardware problem, I think.

If my belief that the battery is malfunctioning seems accurate, where should I purchase a replacement? If something else seems to be the issue, what can I do about it?

I am also considering simply replacing the laptop with something better. What laptops would you suggest?