During the install of windows 10 from windows 8.1, I left my alienware x51 unattended for an hour. When I returned, the screen was black with a movable cursor on the screen. 

Help would be greatly appreciated as I really need this fixed asap. Control+Alt+Delete does not work.

  From Safe Mode w/Networking work through the Windows 10 Install Integrity Checklist.   

If Safe Mode doesn’t work or help stabilize things then return to  Advanced Startup Options in Windows 8 or 10.  Next try Command Prompt  to run Checklist repair commands including sfc /scannow, to see if it will repair and start, or  do a Reset Windows 10.  

There are additional steps here for Troubleshooting Windows 8 and 10 Failure to Start – Microsoft Community
   
 

Better yet do the vastly superior  Clean Install Windows 10 following the steps in the link to delete all partitions down to Unallocated Space to get it cleanest.  After install reactivate with your Product Key, automatically from embedded Product Key if a factory install,  or if free Upgrade has already activated. Activation in Windows 10 – Windows Help.   
 

 At any time you can  Rescue Files when Windows Won’t Start.

If these fail you can try to run Factory Recovery from it’s hotkey at boot; find yours by googling the “PC make/model + Run Factory Recovery.”    Factory Recovery methods