How to merge multiple rows with same data except one column with different data.

Hi ethinix 

With Power Query. Grouping of records based on Latitude & Longitude:

// ZipCodesConcat
let
    Source = Excel.CurrentWorkbook(){[Name="Table1"]}[Content],
    SourceNames = Table.ColumnNames(Source),
    Keys = {"Latitude", "Longitude"},
    TypedZipCode = Table.TransformColumnTypes(Source,
        {{"DELIVERY ZIPCODE", type text}}
    ),
    GroupedByLatLong = Table.Group(TypedZipCode, Keys,
        {
            {"DELIVERY ZIPCODE", each Text.Combine([DELIVERY ZIPCODE], ", ")},
            {"DATA", each Table.FirstN(_, 1), type table}
        }
    ),
    Expanded = Table.ExpandTableColumn(GroupedByLatLong, "DATA",
        List.Difference(SourceNames, Keys & {"DELIVERY ZIPCODE"})
    ),
    Reordered = Table.SelectColumns(Expanded, SourceNames)
in
    Reordered

In attached file:
- Put your data in Table1 (sheet 'Input'), adding your extra column(s) that don't appear on your picture
- Switch to sheet 'Output' > Right-click in table ZipCodesConcat > Refresh

(EDIT) Assumptions made:
#1 [Latitude] + [Longitude] are always provided (no blank/null)
#2 The input doesn't contain something like (otherwise the grouping must be revised):