580EX speedlite not firing

Does the pilot lamp light up? If so can you fire it manually by pressing on it? If the batteries are low it may simply just be taking a while to charge, the camera will not wait for it to be ready to fire and it may seem to be not working. If your flash can be fired manually however, there may be a problem with the cameras shutter or the hotshoe. You can do a basic check by pressing the star button at the rear of the camera, you should get a pre-flash. If not, there is a problem with the cameras hotshoe which you will need addressed by a service centre. If you get a preflash you can next check the cameras shutter by setting the second curtain to sync with the flash. This can be done via the cameras "Custom Function" menu, c-Fn 15. Set the camera to TV mode and chose a 1 second exposure. Take a shot with the flash attached, if the shutter is working correctly, the flash should fire a pre-flash and then a main flash. If it doesnt, the switch inside the shutter is broken and the shutter needs to be replaced. This is a pretty labour intensive repair and you may consider an upgrade as more economical.