I'm really new to VBA so please be really specific with your answer.
The code I've written does a lot of copy and paste functions. Every time I run the code, I get a pop-up box telling me that I have a Clipboard error:
We couldn't copy the content to the clipboard because it's in use by another application. You can still paste your content within this workbook, but it won't be available in other applications.

I have tried Application.CutCopyMode = False and Call ClearClipboard after copying but I still get the message.
This is one of the copy code routines. It just copies the contents of one worksheet to another, in different workbooks:
For Each cell In destinationWorksheet.Range("A1").CurrentRegion
cell.Value = CStr(cell.Value)
Next cell
And this is the other copy code routine, which does a column by column copy in different workbooks:
sourceColumn = 0
For i = 1 To sourceSheet.Cells(1, sourceSheet.columns.Count).End(xlToLeft).Column
If sourceSheet.Cells(1, i).Value = sourceColumnName Then
sourceColumn = i
Exit For
End If
Next i