I know from personal experience, Honda's are notorious for making the clicking sound, lights on and everything all because the cable are not tight enough on the terminals. Matter of fact, I replaced the alternator on the Legend on Thursday night, test drove for about 10 minutes, then pulled back in the garage. I cleaned up the garage and then some minutes later went back to see if car started and it was fine. Next morning came out turned the key and car started fine again. I needed to put the battery tray back in the car so I took the battery out again, put the tray in and when I went to start the car, it was the clicking noise, all lights on but no start. I popped the hood, tightened the cables on the terminals, mind you they were already pretty tight, or so it seemed, and the car started. No problems since.
CHECK YOUR BATTERY CABLES AND TERMINALS. Even if they look tight, tighten them some more.