Why isn't my thermostat working?
The colors are mostly irrelevant - while there is a "standard", really what is important is that when changing the thermostat, you write down what terminals the wires are connected to and that you connect them to the same terminals on a new thermostat.

The "click" of your thermostat is a relay - it is possible that your thermostat is no longer functioning properly.

It is unlikely that two wires would be connected to the same terminal at the thermostat. I would suggest purchasing a new thermostat and ruling out whether the thermostat itself is the issue.  If a new thermostat also does not function, it is likely that there is an issue with the controller board in your furnace, or an issue with the wires running between the two.