Laptop power problem?

I just got an HP 8510p laptop. It had a 150w power adapter and a 14.4v/73wh battery in it. The problem is the laptop will suddenly shut off for no reason. When I try to restart it gets anywhere from 2 seconds into the process to almost booted up then shuts down and automatically tries to restart itself over and over with the same results. This is with me only hitting the power button once. I’ve looked up new batteries and power adapters and they are running 65w on the power adapter and 11.1v on the battery. Should I go this route? Is this what should have been in the laptop to begin with? I forgot to mention right now it seems to be running fine when I pulled the battery and use my uncles 65w power adapter. I’m guessing someone put the wrong equipment with it before they sold it me. Before you go telling me to get rid of it and get a better laptop, No! I just had a new i5 processor, 17in 1tb laptop that I got rid of because I do not use them much but cannot live without one. Besides this laptop looks just like it came out of the box and all the components are almost a match for the one I got rid of at 1/10 the price. I just want to get the power issue straightened out.