Sorry to hear your having that problem. I've had similar Canon cameras apart and am familiar with that zoom-shutter combo switch. The switch itself is both mechanical and activates electrical responses like the zoom and shutter and either or both might be to blame. You could have some dirt or sand inside the switch causing the button not to press down or the switch internally has failed perhaps broken.
Underneath the switch is a flexible printed circuit board that the mechanical parts of the zoom and shutter switch activate. That board could have failed or I have seen those boards come loose in which case the mechanical switch no longer makes contact at all or intermittent contact at times. That would not explain your shutter switch not able to be pressed down. That most likely is either dirt or a failure of the switch.
Having said all that here is what I would try. First take a vacuum and suction out that switch while moving the zoom lever and pressing the shutter button in hopes or removing any dirt inside. Test it's operation if Ok then let it be. If not then get some DeoxIT® Gold G100L, Squeeze Tube soluttion. Drop a couple drops inside the switch and work the lever and button then test it out. You can get the Deoxit spray but you have less control over the application. It is completely safe for all plastics and rubber but you don't want it getting into the lens or sensor so cover the rest of the camera and be careful, pratice first.
Your last resort is sending it in for service
