That "click" we all or most of us hear is generally the unit completing some basic self-diags and then powering up the rest of the unit, the output amp for one.
On mine, it will not "click" if for example the speakers are shorted or there is an unsually high input source.
As advised I would start with the fused, if you are under warranty, then I would not pop the cover, you may well void it. If you are not under warranty then no problem, just the usual safety concerns. The number 1 to start with, IS MAKE SURE IT IS UNPLUGGED from WALL POWER!
Now that we have that out of the way, the fuses should be easy to find and in all but a couple cases, they were not soldered in, they just pop out of the holders.
To test the fuse, you need to remove at least one end from the fuse holder/clip otherwise you may just get a read through the circuit. With one end of the fuse popped out you should see 0 Ohms or very close to it.
Last note might have been the first, but you can also just pull all and I mean all connection except power and see if it "clicks" when you turn it on, this will mean either one or more of your speakers were or are shorted, or one of your input sources was bad.
If it did click, start with your speakers one at a time, hook it up, see if you get a click and better yet, tune in a radio station ans see if you get sound. Repeat for each speaker. The repear for each input device, like DVD Player, CableTV Box, whatever you have.