If the cracks aren't too bad, can't you just lay some pressure treated 2x4 sleepers right on top of the slab?
If the slab has cracked and sunk unevenly, see if any local contractors do 'hydro-jacking' - they pump some concrete underneath the slab - not a ton of concrete - just enough to raise the sunken part back to its original level. Make sure you eliminate the source of the cracking, or your son may have a geyser in his bedroom.
Then, I still say lay some pressure treated sleepers directly on the slab. (first put down a vapor barrier) - Lay the sleepers on their sides (i.e. so they are 3.5 inches wide and 1.5 inches tall.) - space 16 or 24 o.c. You might consider radiant floor heating also.