Unlocking 720, 4th core crashes on window welcome screen

Yes, it is unlockable, but it might faulty (functioning with defects, or limited functionality).

It seems there is a notion out there that of a core being "unlockable" is synonymous with "fully functioning", which is not the case.

If the core is non-functional (dead) it will not unlock, or rather, the computer will not function with BIOS set to use this dead core.
If the core is functional, it may be fully working or it may be faulty.

The Semperon 140, X2 550 and X3 720 all seemed to have one or two locked cores, but some have fully working locked cores while others have faulty locked cores. It's the luck of the draw. (I say locked cores to refer to the cores not normally used, but are present).

Increase vcore up to what you feel comfortable with and see. Take it off Auto and manually set your voltage, try to boot. If that's not doing it for you, the core is faulty, so best leave it locked (back to X3).