You should be able to run it on the PSU - for the HDD I can't really think of anything, except see how far it gets in the boot sequence (not knowing how broken your current HDD is though that's a long shot).
As you'll obviously be taking it apart you could visually inspect for damaged components in the power area (but it it works from the PSU they are probably OK).
Not really sure what you can do with a multi meter though.