This issue has been seen where the computer has a corrupt or conflicting version of libcurl.dll in the C:\WINDOWS\System32 directory.
Non-system software applications should not be installing DLLs to the C:\WINDOWS\System32 directory.
On the system that this issue was seen on, some users were not aware of what application had placed the libcurl.dll file in the system32 directory.
Deleting or renaming the libcurl.dll file in the C:\WINDOWS\System32 directory allows Vivado Design Suite to open and run correctly.
Xilinx recommends that the libcurl.dll in the C:\WINDOWS\System32 directory be renamed and then replaced with the version from the Vivado install.
This will allow any application referencing the DLL to continue to work.