A clue as to what event (and/or where it is) might help, as Me might not be applicable. Was going to suggest that the function call might be where the issue lies (because the FileSystemObject method is CopyFile but you have FileCopy) but you've indicated the 2nd line is the one that generates the error. Hope you're sure about that because unless you declared DestinationFile as some type of object, the error doesn't make sense to me, based on what I'm reading. Did you determine that by stepping through the code?
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.