Windows – Oracle Forms 6i on Windows 7

You have to initiate the duplicate from the target database to be able to connect to the not mounted target database. I suggest you to downgrade the oracle version on the 64 bit machine. The easiest way to do this will be to install 11.1.0.6.0 version on the 64-bit server into a separate oracle home and perform the duplicate. You can upgrade the database after duplicate and switch it to the 11.1.0.7.0 home.

The error you are getting on the 32-bit database seems to be a connection problem to the database. The target instance is not mounted and you cannot connect to is via SQLnet.

When performing the duplicate form 64 bit system, please make sure that you are using username/password in the connection string to the target database and not the system authentication.

Best regards, Yuri

O/S-Error: (OS 665) The requested operation could
  not be completed due to a file system limitation

So the windows error 665 is the reason for the error an the error refers to file C:\ORADATAFILES\ORAPROD03\USERS03.DBF.What is the problem with the file? The following article discusses this error message: What factors can lead to Win32 error 665 (file system limitation)?. If the reason is file fragmentation a patch is available. I know it is to late but maybe a restore will not be necessary in this situation.