Slab foundation.

[Billhart]

Is this a slab with monolithic footers (turned down edge)? Frost walls with slab on grade? Post tensioned slab? Slab supported by piers? and there are probably a couple of other combinations that I am not familar with.

and what about internal load bearing walls? they might not fall at the same place that the old house has footing under the slab.

You really need someone local that can inspect what you have and knows local soil conditions. they may have to run some engineering test on the slab and soil.

It may not be practical to reuse the existing slab.