Nikon coolpix S3000 won't take a picture when the

Assuming you have new batteries and the camera lens cover is opening when turned on. Try switching to any mode other than automatic, turn off the flash, and press the shutter button. 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

Mine stopped taking pics and the ed light would come on, but what I noticed is if I push the shutter button down hard, it took pics normally. I guess over time debris gets caught up under the shutter button.

I had the same issue and resolved it by deleting all of the pictures off of the existing memory card. It had pictures on the card from another camera. It worked fine, then.