My understanding is if it were the hard drive it would crash quickly. Probably a fan.

I lost my first PC when papers got piled around it and it over heated, so I have been pretty particular about stuff like that over the years.  I put a card slot fan in my off line only computer for extra airflow.  Recently it started squalling and like you I figured the hard drive was going. That is when I was told when they fail they don't warn you.

I opened it up and cleaned all the dust out. Started it up with the case open and found it was my add on fan. I replaced it and things are working great.