I would test again with a different iso and see if the problems persist.
If they do (and I suspect that they will, since you report similar problems with Windows) then I would suspect the motherboard, since the SMART test did not report errors.
Unfortunately I don't know of any good tools for testing/reporting that deal with motherboard hardware. A quick search turned up Phoronix Test Suite but that appears to be more focussed upon benchmarking rather than troubleshooting. I will try it out and report back later.
I have a fairly flaky motherboard on my desktop machine. It's caused lots of problems over time, but I found that replacing some power-hungry components and installing a better PSU has rendered it a great deal more reliable. In any case of mysterious errors like those you're experiencing I recommend reviewing your machine's power budget.