If the slab is in good condition ( no large cracks and not heaved up) I would be sorely tempted to pour a 12 inch or so base on top of the slab ( the base keyed into the slab and caulked in between) and then build the wall ( or repair it ) on that using a sill plate gasket ...
This is a quick, relatively easy, and cost effective solution. I had a similar problem with a carport that was incorporated into my house, simply by laying 2x's on the old carport slab then building walls on top. Then someone in their brilliance poured a concrete apron, and added an asphalt walkway right up to the walls. Since permitting in my area is a major pain, I discussed the situation with a good contractor I was lucky to hook up with. They supported the roof, cut away the bottom of the wall studs and removed the old plate which carpenter ants had been working on, then poured a 6x6 stem wall around the perimeter. After reframing and tweaking the siding it appears to be a standard foundation wall, barring educated close inspection. The height of the stem wall will depend on the landscape features adjacent the walls, just make sure it's tall enough to prevent water reaching the sill plate and use a treated plate.
While we only get limited freezes, and rarely enough to cause any heaving, this solution has worked well for 7 years now without any problems.
