If you need to do it without linq, you can try this.
NOTE: I did just hammer this out here, I haven't thoroughly checked the syntax.
private void RemoveEmptyRows(DataTable source)
for( int i = source.Rows.Count; i >= 0; i-- )
{
DataRow currentRow = source.Rows[i];
foreach( var colValue in currentRow.ItemArray)
{
if( !string.IsNullOrEmpty(colValue) )
break;
source.Rows[i].Delete();
}
}
}