POST cards are great to have in general, but I don't think in this situation they are going to detect anything. i.e. the problems happen after it's gone past the basics. POST is over when you see the "POST" screen, any recoverable errors it reports (key stuck, CMOS check) and any non-recoverable is where it sticks and the POST card gives you a clue.
Edit: Okay reread, you have some occasions of not making it to the POST screen? Sorry, I may have confused your "not booting" statements with seeing POST screen and then doing nothing. or having the storage interface problems. So yeah if you are looking at a blank screen, maybe a blinking cursor, then the POST card should say something.
Unicorn herding operations are proceeding, but all the totes of hens teeth and barrels of rocking horse poop give them plenty of hiding spots.