Harley won't start, just a click when I push the start button?

Well for starters "looks good" isn't good enough.You need to remove both battery cables at both ends and clean the connections as a very first step.Then i advise you get a cheap volt meter.With it you can check for resistance in the battery cables themselves.A cable can look good and still be bad inside.Set it to ohms and put a test lead at each end of the cable.There shouldn't be any resistance.Hook everything back up turn the key and and check the voltage at the starter solenoid.It should read about the same voltage at the starter end of the cable as it does at the battery.For that the meter should be set to dc voltage and 20 volts if it's not an auto ranging meter.Make sure the black test lead is on a good ground on the bike.Start by doing all that and get back to us with the results.The fact your getting a click means it wants to crank over.It either is suffering from a low voltage problem at the starter or the solenoid or starter is bad.Also did you try tapping on the solenoid lightly to see if it makes a difference?