You would do it this way:
Range("C" & processRowBegin & ":C" & processRowEnd).Select
Range takes either two cells or a string to denote the extents.
To do it by the two cells:
Range(Cells(processRowBegin,3),Cells(processRowEnd,3)).Select
A couple notes:
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One should avoid using select and simply do what is desired with the cells. For more information on how to avoid it see this POST
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One should always qualify all all range objects to their parent sheets. If using the Cells() they too need to be qualified
Example
With WorkSheets("Sheet1")
.Range(.Cells(processRowBegin,3),.Cells(processRowEnd,3)).Value = .Range(.Cells(processRowBegin,5),.Cells(processRowEnd,5)).Value
End With