MacBook Pro only turns on when power button held down and more

Hello, hope you guys can help!

In addition to the title, whenever the MagSafe charger is plugged in, 90% of the time the entire system shuts off. If I press the power button, the laptop starts to boot up but dies soon after reaching the Apple logo. When on (after holding down the power button), the OS is incredibly laggy and slow to respond with a ~7 second delay. Kernel_task is running at 300-600% CPU, but fan is not on and the laptop itself is not hot.

I have attempted a PRAM reset as well as an SMC reset, but neither has done anything to resolve the issue. This makes me think there is a hardware issue that is somehow related to the CPU, the power supply, and perhaps a thermal sensor?

Thanks much!

S