If nothing is connected to any of the pins and it goes into latchup on powering up,
you fried it.
Its really important to remove power fast when latch up happens as lots of heat
is generated. And of course its important to figure out why it happened so you
don't trigger it again - usually its because of rogue voltage to one of the pins, which
should never go outside the supply range.
All CMOS devices are susceptible to latch-up, although it can be mitigated by
certain design techniques (this is normally done to ruggedize power electronics,
not for a microcontroller which is not expected to be subject to abuse).
The process used in the Due is a 1.8V process with 3.3V I/O circuitry, there is
absolutely no tolerance to higher voltages, not even for a microsecond.