I'd say utri007 was correct, I've just popped my old Blizzard060 board into an A1200 with 3.0 Roms and with an old PSU that made the same whining sound as you describe. Guess what same problems you report with random results.
Then I powered up the same machine using an old converted PC power supply and the problems are gone, boots up fine every time with no random crashes...
I'd known about this problem before and thought I'd just check to make sure, your best bet is to buy a PC power supply and make your own one up then you'll have plenty of power to add whatever you want in future to you miggie....
Just a shame Mechy's sold out of his neat compact PSUs or that would have done the trick for you...
