Everything seems fine with your camera, except that when you press the shutter button nothing happens! On Canon cameras you may also notice flashing yellow/orange lights by your viewfinder. Try switching to any mode other than automatic, turn off the flash, and press the shutter button. Did the camera take a picture? If so, continue reading.
Many cameras have a safety feature that prevents the flash capacitor from charging if the case is opened. This is to lessen the chance of electric shock. They usually use one or two of the screws along the perimeter of the camera to complete a circuit that lets the processor know that the case is closed. Verify that all the screws are in place along the perimeter of your camera, and that there are no gaps along the perimeter seams. If you're missing a screw, try using one of the others to replace it.
If they're all there, next thing to check is the batteries. The brand that you're using may have reached its shelf life, or just may not have sufficient power to charge the flash capacitor. Try a better brand, or better yet rechargeable NiMH batteries.
If the above didn't help, then the flash tube or its circuit is probably at fault. In this case, would then recommend professional repair. This repair is somewhat difficult, requires some soldering, has some danger of electrical shock, and goes beyond what I'd like to describe here.
Digital cameras for the most part should only be used with rechargeable NiMH batteries. These days many retailers sell these for around $7 for a package of four (about $15-19 for the batteries with charger). Keep in mind they'll save you big bucks in the long run over alkalines, AND they'll last for at least 100 pictures per charge (and probably many, many more). You'll be very pleased with their performance, and may slap yourself for not buying them sooner. When at the store, look on the package for a power rating of at least 2500 mah.