Did you upgrade from Windows 7 to Windows 8 or another Windows version? If you upgraded from Windows 7 to Windows 8, you may need to update your system BIOS.
If the black screen is showing up before you've upgraded to Windows 8, you will be able to upgrade your laptop to the latest version of BIOS by downloading the update. If the black screen is showing up after you've upgraded to Windows 8, there will be two options for getting the latest system BIOS. You can refer to this guide for the different fixes: http://www.dell.com/support/article/us/en/04/SLN116332/en