I turn on my camera and it just shuts itself down

Then lens assembly could be stuck, or the battery could be low or weak. Make sure, first, that the contacts inside the battery are clean (clean them with a qtip and isopropyl alcohol). There's a couple of web sites that explain what things you can try to get it working, and they say about half the cameras can be made to work trying their suggestions:
http://camerarepair.blogspot.com/2007/12/fixing-lens-error-on-digital-camera.html
Even though the title of this page is lens errors, it applies to "stuck lens", and has steps to take to try to fix it.
This site is for battery problems, which is the other thing that might be going on with your camera:
http://camerarepair.blogspot.com/2007/11/simple-fix-for-dead-cameras-that-wont.html
Try these things, and you have a good chance of getting the camera working again.