Could be various things that cause it to not turn on, but the most likely cause will be a blown fuse. Will have to check for your specific car where the fuse is located for the stereo. There is also a fuse on the rear of the stereo itself on some models so this may be worth a look. Other than that it could simply be a faulty stereo or loose wiring at the back of it.
The easiest way to check a fuse without the proper equipment it to pull it out an visually check if you can see a break in the wire in the plastic part between the 2 metal prongs.