Function ColumnNameToNumber(oSheet As Object, columnName As String) As Integer
    ColumnNameToNumber = oSheet.getCellRangeByName(columnName & 1).getCellAddress().Column
End Function

Function CountMoney(oSheet As Object, dateColumn As Integer, moneyColumn As Integer, startDate As Date, endDate As Date) As Double
    Dim oCells As Object : oCells = oSheet.getColumns().getByIndex(dateColumn)
    Dim oNotEmpty As Object : oNotEmpty = oCells.queryContentCells(com.sun.star.sheet.CellFlags.DATETIME)
    Dim nrows As Integer : nrows = oNotEmpty.computeFunction(com.sun.star.sheet.GeneralFunction.COUNT)

    For i = 0 To nrows - 1
        Dim rowDate As Date : rowDate = CDate(oSheet.getCellByPosition(dateColumn, i).Value)

        If startDate <= rowDate And rowDate <= endDate Then
            answer = answer + oSheet.getCellByPosition(moneyColumn, i).Value
        End If
    Next

    CountMoney = answer
End Function

Sub Main
    Dim oSheet As Object : oSheet = ThisComponent.Sheets(0)
    Dim inputString As String
    Dim components() As String

    inputString = InputBox("Enter 'dateColumn,moneyColumn,startDate,endDate': dates are in format MM/DD/YYYY, columns are column letters")
    components = Split(inputString, ",")

    Print CountMoney(oSheet, ColumnNameToNumber(oSheet, components(0)), ColumnNameToNumber(oSheet, components(1)), CDate(components(2)), CDate(components(3)))
End Sub