Unexpected Shutdowns even after complete reset/reinstall.

"Your computer shut down because of a problem."

It began while CPU levels were high, occasionally while working with an external hard drive. Random shut downs which turned into prohibatory symbols and blank restart screens. I reset PRAM, SRC and many times I was unable to even get past the login screen.

I performed a complete erase/reinstall of macOS, but I am still experiencing sudden shut downs after working for a minute or two, and I haven't re-installed any of my non-factory applications. It's now clean, as-new and causing these shut downs.

My MacBook Pro is only around 2 years old, but it is not covered by AppleCare. All online tutorials tell me that if my problems occur even after all the diagnostics and resets, it must be a hardware issue. Can anyone give me advice as to how, as a consumer, I can further investigate the hardware before having to pay out of pocket for a diagnosis?

It may help to mention that prior to these issues, my power adapter would chime intermittently, and power seemed to cut in and out. Other USB devices also had trouble mounting. I thought the PRAM/SRC resets would clean up any USB bugs in case they're related to the crashes, but as I stated, my problems continue.

I'm up and running, but I fear that within a minute of use, it will crash again.

Any help beyond the many self-diagnostic tutorials that stop at reset/reinstall would be greatly appreciated.