The steering wheel issue is CERTAINLY suspect. You can easily determine a draw with a test lamp and multimeter.
Another way is simply pull out the horn relay. That is what would be happening. Even if you unhook the horn itself, the relay is being activated.
But what you are not saying is.........what happens when you charge the battery? Does it crank? If not, still could be bad connections / cables AND STILL COULD BE a bad (defective) battery. "New does not mean functional." As I said, getting the battery load tested is a good idea. Lacking that, temporarily swap a suspect battery into a known working car and see if it will crank that car OK
