Remove the backup and try to turn it on (the calc works without backup) to be sure it's the correct backup.
Replace the AAA batteries too to double check it's not the batteries (but if you see the black box I think it's not a AAA batteries issue).
You can reset the calc by putting battery and removing it quickly multiples times (you will loose all your data but you probably already lost everything but the flash if your calc has flash).
If even after this operation you can't turn it on, contact the reseller and ti care customer service. There's probably an hardware problem.
Maybe someone else has better ideas?