You have to make sure the cable is good at BOTH ends. As was said, the click indicates that your solenoid is being activated. Either there is no power getting to the solenoid high current connection, or the solenoid is bad.
First test, jam a pair of pliers between the big leads on the solenoid, and see it it activates the starter. (Make sure the bike is in neutral.) If the starter spins, it means you have continuity through your cables and most likely the solenoid needs to be replaced. Take your old solenoid to a local NAPA auto parts store, and they should be able to match one up for you for a lot less than Suzuki would charge for the part. (The solenoid is a standard electrical part that Suzuki does not actually make.)