It sounds as if the lens is not extending completely at power-on.
It should extend far enough to lock in place before anything will work.
That can happen if the camera has been dropped and it can happen if a grain of sand has gotten into the gearbox. Think back where you have been before the problem developed.
You can try an experiment;
When you power-on the camera and the lens starts to extend, grasp the lens housing and gently pull. See if that lets the lens extend further into locked position. If so, the camera should then work.
Have a Canon Powershot S5 IS. With fresh batteries and a SD card installed, the camera will power up to shooting or playback mode (that is, the orange or green light will come on; when switched on to shooting mode the lens does extend). But nothing else will happen. You cannot turn it off, nothing appears on the viewfinder or the LCD screen. You cannot take a photo or playback any photos. The only way to turn it off is to open the battery door. I have tried three different sets of batteries, including fully charged NiMH and normal alkaline batteries.
The camera had been working fine using the same set of rechargeable batteries a few days ago.
Thanks for any help!