Two totally separate problems by the sound of it...
The screen is a physical problem of some sort, it could be a faulty display panel, in which case replacement is only answer, or it could be as simple as a bad connection on the cable that connect the display panel, in which case just taking it apart (not always easy) and remaking the connections will fix it. or worst case it could be the graphics controller on the main board gone faulty and the main board needs replacing.
The not starting up is unrelated and could be lots of things, are there any error messages at all on startup?