The click to be heard is very faint. If you can hear the click, it is probably a bad flash tube. Otherwise it is likely a trigger coil failure, as the unit is getting charged (indicated by the green light). If you still do not hear the click, then the light would need to come in for service. If the light is less than 2 years old, then the repair and shipping from us to you would be covered under warranty. please see this link for our address and a link to our repair forum (please send it to the Tennessee address if you are in the U.S.).
http://www.alienbees.com/contact.html#repair