You can do this very quickly if the cells are truly blank using SpecialCells
Manual
Select Column C
Press F5, then Special
Check Blanks, then OK (see this step in the pic at bottom)
Delete the rows that are now selected (e.g. right click in selection > Delete cells... > Entire row or via the ribbon (see second screenshot))
VBA
`Sub QuickCull()
On Error Resume Next
Columns("C").SpecialCells(xlBlanks).EntireRow.Delete
End Sub