Help to solve the below logic using power bi

If I interpret the logic correctly, then you need:

all records with status "Completed", and

all records with status "Failed"

       if there is no record for the same person with status "Completed" within +/- 4 hours

all records with status "Incomplete"

       if there is no record for the same person with status "Completed" or with status "Failed" within +/- 4 hours

I put your data in an Excel file and created the Power Query (M) code below.
To be honest I have my doubts about performance, but you may give it a try on some test data.

let
    Source = Excel.Workbook(File.Contents("C:\Users\Marcel\Documents\Forum bijdragen\Power BI Community\Help solve logic.xlsx"), null, true),
    Input_Table = Source{[Item="Input",Kind="Table"]}[Data],
    Typed = Table.TransformColumnTypes(Input_Table,{{"DateTime", type datetime}, {"Name", type text}, {"Status", type text}}),
    #"Added Custom" = Table.AddColumn(Typed, "Keep", 
                                        (x) => if x[Status] = "Completed" 
                                               then true
                                               else if x[Status] = "Failed"
                                                    then 0 = Table.RowCount(Table.SelectRows(Typed, each [Name]     =  x[Name] and
                                                                                                         [Status]   =  "Completed" and 
                                                                                                         [DateTime] >= x[DateTime] - #duration(0,4,0,0) and
                                                                                                         [DateTime] <= x[DateTime] + #duration(0,4,0,0)))
                                                    else 0 = Table.RowCount(Table.SelectRows(Typed, each [Name]     =  x[Name] and
                                                                                                         ([Status]  =  "Completed" or [Status] = "Failed") and 
                                                                                                         [DateTime] >= x[DateTime] - #duration(0,4,0,0) and
                                                                                                         [DateTime] <= x[DateTime] + #duration(0,4,0,0)))
                                        ),
    #"Filtered Rows" = Table.SelectRows(#"Added Custom", each ([Keep] = true)),
    #"Removed Columns" = Table.RemoveColumns(#"Filtered Rows",{"Keep"})
in
    #"Removed Columns"