Concrete floor surface finishing
As Kris already indicated with a link in a comment, the solution for "big" equipment is usually not Home Depot. Some Home Depot rental departments are better than others, so you may have better luck if you check other area stores. But there are plenty of places where the only thing they do is rent equipment, so they:


have a larger variety of equipment available than an "everything" store
often have lower prices, since this is their specialty
are more likely to have someone on staff who can give a little advice instead of being just an order-taker


A typical place won't require anything special to rent a floor polisher or most other equipment, though it helps if you come in seeming reasonably knowledgeable about what you are trying to do and what kind of equipment you need.