The starter solonoid on the start is probably bad. take a hammer and tap the starter several times ont he side of it, doesnt need to be hard. Then try to start it. 90% of the time it will start after that.

If that works that means the starter is going bad. And if that doesnt work, the starter can still be going bad. Ha.

My money is on the starter being bad if the battery is new with clean cables. The click sound is the solonoid closing up on the firewal, but the solonoid on the starter is not.