The screen on my camera stays black after the camera is turned on. The lens cover is open. If I take a picture it will just be black.

If you transfer the picture to your computer and you get a black image then your "lens" is faulty - actually a cmos based receiver.

If the photo is ok - then the back LCD screen is at fault.

Either way, it needs fixed and if under guarantee contact the manufacturer and ask for a replacement, or take it back to the store you got it from.

Or if out of warranty you will need to buy a new one I am afraid.
If you have some technical skills you could look on eBay for another broken one of the same model as yours and put the two together to get a working camera.