I thought when the sentence needed a subject it was always 'det.' Am I wrong?
You're right, but this is not a placeholder subject, this den actually refers to an object previously mentioned, so without context it could be either den or det here.
If i were to say it is in that other cabinet i would have been "den/det är i det där andra skåpet"?
How could you say "It is in the second cabinet"? And could the sentence start with "det är"?
That'd be the same sentence, since andra means both second and other.
Yes, the sentence could start with det är.