Was the `new` drive exactly the same as the failed unit or was it slower?
Does the PC start OK (first time) in Safe Mode?
Have you done all updates to Windows and security software since you did the backup?
If you leave the PC when the `black screen` appears, does anything else appear, such as a `no signal` message from your monitor? Also does it just `hang` at this point if left or what?
Which dlls does it tell you are missing/corrupt? Try to make a note of them.
Have you tried running sfc /scannow? click here. It may cure the problem but if not at least it will check all files for you in case your backup let you down (unlikely). I presume the backup was verified?
As a last resort, you could try reinstalling the backup image.