Should a computer be left on for long periods?

There is no serious drawback, for the computer, if you leave it on for a long time. You may want to turn the computer off (or suspend it, or hybernate it) while you don't need it, to save energy. If you need the computer to process something while you are away - for instance, to download a file, or to do some long calculation - you can turn the screen off; the computer doesn't need the screen for its work.