Text to Date has the wrong year

You need to combine (i.e., merge) with year data and then convert to date type.

I copied your sample data in M query and did this ... 

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WMjIwMqoxrDHW9UrMq7EEkUqxOlBhoIQBWNzQDFXCuMbQHCxhZIwqYVJjZAKWMDaASMQCAA==", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [#"Year|Week_Num|Start Date|End Date" = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"Year|Week_Num|Start Date|End Date", type text}}),
    #"Split Column by Delimiter" = Table.SplitColumn(#"Changed Type", "Year|Week_Num|Start Date|End Date", Splitter.SplitTextByDelimiter("|", QuoteStyle.Csv), {"Year|Week_Num|Start Date|End Date.1", "Year|Week_Num|Start Date|End Date.2", "Year|Week_Num|Start Date|End Date.3", "Year|Week_Num|Start Date|End Date.4"}),
    #"Renamed Columns" = Table.RenameColumns(#"Split Column by Delimiter",{{"Year|Week_Num|Start Date|End Date.1", "Year"}, {"Year|Week_Num|Start Date|End Date.2", "Week_Num"}, {"Year|Week_Num|Start Date|End Date.3", "Start Date"}, {"Year|Week_Num|Start Date|End Date.4", "End Date"}}),
    #"Inserted Merged Column" = Table.AddColumn(#"Renamed Columns", "Start Date 2", each Text.Combine({[Start Date], [Year]}, "-"), type text),
    #"Inserted Merged Column1" = Table.AddColumn(#"Inserted Merged Column", "End Date 2", each Text.Combine({[End Date], [Year]}, "-"), type text),
    #"Removed Columns" = Table.RemoveColumns(#"Inserted Merged Column1",{"Start Date", "End Date"}),
    #"Changed Type1" = Table.TransformColumnTypes(#"Removed Columns",{{"Year", Int64.Type}, {"Week_Num", Int64.Type}, {"Start Date 2", type date}, {"End Date 2", type date}}),
    #"Renamed Columns1" = Table.RenameColumns(#"Changed Type1",{{"Start Date 2", "Start Date"}, {"End Date 2", "End Date"}})
in
    #"Renamed Columns1"

Output:

Hope it helps!