Hey Sam,

This below code is what I was able to modify (By adding an "if" statement comparison) and it seem to work. my earlier code had a lot of redundancies. I don't know how to optimize it though. But the below code works flawlessly now. Marking the thread as solved 
Sub Merge_Average()

'General variables
Dim StartTime As Double
Dim myPath As String
Dim myExtension As String
Dim FilePicker As FileDialog
Dim MinutesElapsed As String
Dim Average As Double
Dim Value As Double


'Table file variables defined below
Dim wb1 As Workbook ' Table Workbook
Dim taTimesRng As Range
Dim taStartTime As Double
Dim taEndTime As Double
Dim taCell As Range
Dim currentColumnTa As Integer                                                  ' current column number in "Table" File
Dim columnHeadingTa As String                                                   ' current column name in "Table" File
Dim taCellRow As Long
 
'Data file variables defined below
Dim wb2 As Workbook  ' Data Workbook
Dim daStartCell As Range
Dim daEndCell As Range
Dim daStartRow As Long
Dim daEndRow As Long
Dim currentColumnDa As Integer                                                   ' current column number in "Data" File
Dim columnHeadingDa As String                                                    ' current column name in " Data" File
                                                  
StartTime = Timer    ' Countdown clock


Set wb1 = ThisWorkbook


    Application.ScreenUpdating = False                                          ' Switching this to False optimizes Macro Speed.
    Application.EnableEvents = False                                            ' This blocks any popups
    Application.Calculation = xlCalculationManual                               ' This optimizes the processor output


Set FilePicker = Application.FileDialog(msoFileDialogFilePicker)
            With FilePicker
                    .Title = "Select A Target Folder"
                    .AllowMultiSelect = False
                        If .Show <> -1 Then GoTo NextCode
                        myPath = .SelectedItems(1) '& "\"
            End With
                                                                                
NextCode:
    If myPath = "" Then GoTo ResetSettings


Set wb2 = Workbooks.Open(Filename:=myPath)
Set daEndCell = wb2.Sheets("Data").Range("B3")


wb1.Activate
Set taTimesRng = wb1.Sheets("Table").Range(Range("B3"), Range("B3").End(xlDown))
For Each taCell In taTimesRng
    taStartTime = taCell
    taEndTime = taCell.Offset(, 1)
    taCellRow = taCell.Row
    Set daStartCell = daEndCell
 
   
    Do While daStartCell < taStartTime
        Set daStartCell = daStartCell.Offset(1)
    Loop
    Set daEndCell = daStartCell
     
    If daEndCell.Offset(1) = "" Then GoTo ResetSettings
    Do While daEndCell.Offset(1) <= taEndTime
         
        Set daEndCell = daEndCell.Offset(1)
    Loop
     
        daStartRow = daStartCell.Row 'Top row of time bracket
        daEndRow = daEndCell.Row 'Bottom row of time bracket
If daEndCell <= taEndTime Then        ' This additional if statement modification after the start and endrow loop made all the difference
    
        currentColumnTa = 4
        columnHeadingTa = wb1.Sheets("Table").Cells(1, currentColumnTa).Value
        ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
        'Loop and match column headers in Data and Table, compute and copy average values then paste in Table sheet and then loop through rows with start and end time
        ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
        Do While columnHeadingTa <> ""
            currentColumnDa = 3
            columnHeadingDa = wb2.Sheets("Data").Cells(1, currentColumnDa).Value
                  
            Do While columnHeadingDa <> ""
                wb2.Activate
                With wb2.Sheets("Data").Select
                                                                                                 
                        If columnHeadingDa = columnHeadingTa Then
                           Average = Format(Application.WorksheetFunction.Average(Range(Cells(daStartRow, currentColumnDa), Cells(daEndRow, currentColumnDa))), "0.000")
                                      
                           DoEvents
                           wb1.Activate
                           With wb1.Sheets("Table").Select
                                ActiveSheet.Cells(taCellRow, currentColumnTa).Value = Average
                                                                                                
                           End With
                                                                        
                           GoTo MasterFile
                                                                
                        End If
                            
                End With
                currentColumnDa = currentColumnDa + 1
                columnHeadingDa = wb2.Sheets("Data").Cells(1, currentColumnDa).Value
            Loop


MasterFile:
             currentColumnTa = currentColumnTa + 1
             columnHeadingTa = wb1.Sheets("Table").Cells(1, currentColumnTa).Value


        Loop
End If
Next taCell
             ' Determine how many seconds the code took to run


ResetSettings:                                                                  ' Reset Macro Optimization Settings
                                                                              
    Application.EnableEvents = True
    Application.Calculation = xlCalculationAutomatic
    Application.ScreenUpdating = True


MinutesElapsed = Format((Timer - StartTime) / 86400, "hh:mm:ss")
MsgBox "Task Complete!. This code ran successfully in" & MinutesElapsed & " minutes", vbInformation


End Sub