1st , check if there is fuel on fuel line , I believe your car has injector(s), check for power and ground on the injector wires , one of those wire will be the control side which will flash as you crank the motor. might be a good idea to check your fuel injetion fuse and relay.
though your sure that the battery is good and fully charge, battery connection must be checked as a weak connection could easilly cause same symptom. once thats checked and found good, then move to starter to check battery power on the bigger wire. if ok, then try to jump the two wires momentarilly. if all its doing is still just clicking, do replace the starter assembly.