There are a lot of elements that make a strong concrete floor:
1. The thickness of the concrete is not everything, what is important is the concrete mix design, all concrete is designed to meet a certain psi rating. If the psi of your floor is less than the load of the lift and the car, the floor will crack.
2. It is not a good idea to just pick up a jackhammer and go to town, you may damage rebar, post tensioning cables, etc. If you do this you will compromise the structural integridity of you slab which is far worse than any damage that may be caused by the weight of the lift. A pacometer test can be done to find location of rebar. (similar to a bone x-ray) What ever you do - do not damage any rebar!
3. The compaction is also very important as mentioned by Jon B, Chances are underneath your slab you have an engineered fill such as decomposed granite which is a typical underslab material. My guess is this is not your problem.
My first step would be to track down a set of As-built drawings for your house this will tell you exactly what you have; slab thickness, psi rating, underslab material and thickness, rebar location, PT cables (if any), footing locations, thickened edges etc. Then compare this data to the requirements of the lift company.
Also contact a structural engineer in you area and pick his brain over the phone!
Good Luck!