Question : Problem: machine has developed a mechanical whine when starting cold

Machine dates from fall 2005 except one HD which is about 5 years old. Within the last weeks, when starting it whines as if under stress when starting cold. Solution is to shut down cold when it reaches the sign-on screen. Then it starts up normally. I can live with this minor nuisance but is it a harbinger of something about to fail?
Every month I practice the following hygiene: disk defragmention plus error-checking (GUI chkdsk). I have tightened all internal cable connections.
Possible coincidence: at start-up, an empty partition on the older HD claims to need error-checking. Because the partition is empty, error-checking is fast, but it demands it every time. Is there a way of switching off the bit that marks the partition as dirty?

Answer : Problem: machine has developed a mechanical whine when starting cold

Yes, a worn bearing in a fan or drive.
Don't forget about the fans in the power supply. They wear out too.
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This might sound goofy and red-neck (because it is) but you'll be surprised how well it works.
One of the best ways to narrow this down is with the cover off and using a make-shift stethoscope.
All you need is a 2 or 3 foot piece of small diameter tubing. Put one end on/near the suspected problem and the other end (carefully) in your ear. - I have used this method to chase down noises in engines and motors. It works very well inside computer cases too.