Merging workbooks into a new file

Your code almost works as is, just needs a couple of slight tweaks. I also agree with @AnalystCave that if this is a repeating exercise, you may consider a more streamlined solution. But this will work for you.

EDIT: changed to deal with existing destination file -- if it exists and is open, then connect to it otherwise open it; then delete all sheets in the existing file to prepare for the copies

Option Explicit

Function IsSheetEmpty(sht As Worksheet) As Boolean
    IsSheetEmpty = Application.WorksheetFunction.CountA(sht.Cells) = 0
End Function

Sub GetSheets()
    Dim Path, Filename As String
    Dim Sheet As Worksheet
    Dim newBook As Workbook
    Dim appSheets As Integer
    Dim srcFile As String
    Dim dstFile As String
    Dim dstPath As String
    Dim wasntAlreadyOpen As Boolean

    Application.ScreenUpdating = False  'go faster by not waiting for display

    '--- create a new workbook with only one worksheet
    dstFile = "AllSheetsHere.xlsx"
    dstPath = ActiveWorkbook.Path & "\" & dstFile
    wasntAlreadyOpen = True
    If Dir(dstPath) = "" Then
        '--- the destination workbook does not (yet) exist, so create it
        appSheets = Application.SheetsInNewWorkbook  'saves the default number of new sheets
        Application.SheetsInNewWorkbook = 1          'force only one new sheet
        Set newBook = Application.Workbooks.Add
        newBook.SaveAs dstFile
        Application.SheetsInNewWorkbook = appSheets  'restores the default number of new sheets
    Else
        '--- the destination workbook exists, so ...
        On Error Resume Next
        wasntAlreadyOpen = False
        Set newBook = Workbooks(dstFile)             'connect if already open
        If newBook Is Nothing Then
            Set newBook = Workbooks.Open(dstPath)    'open if needed
            wasntAlreadyOpen = True
        End If
        On Error GoTo 0
        '--- make sure to delete any/all worksheets so we're only left
        '    with a single empty sheet named "Sheet1"
        Application.DisplayAlerts = False            'we dont need to see the warning message
        Do While newBook.Sheets.Count > 1
            newBook.Sheets(newBook.Sheets.Count).Delete
        Loop
        newBook.Sheets(1).Name = "Sheet1"
        newBook.Sheets(1).Cells.ClearContents
        newBook.Sheets(1).Cells.ClearFormats
        Application.DisplayAlerts = True             'turn alerts back on
    End If

    Path = "C:\Temp\"
    Filename = Dir(Path & "*.xls?")  'add the ? to pick up *.xlsx and *.xlsm files
    Do While Filename <> ""
        srcFile = Path & Filename
        Workbooks.Open Filename:=srcFile, ReadOnly:=True
        For Each Sheet In ActiveWorkbook.Sheets
            '--- potentially check for blank sheets, or only sheets
            '    with specific data on them
            If Not IsSheetEmpty(Sheet) Then
                Sheet.Copy After:=newBook.Sheets(1)
            End If
        Next Sheet
        Workbooks(Filename).Close (False) 'add False to close without saving
        Kill srcFile                      'deletes the file
        Filename = Dir()
    Loop
    '--- delete the original empty worksheet and save the book
    If newBook.Sheets.Count > 1 Then
        newBook.Sheets(1).Delete
    End If
    newBook.Save
    '--- leave it open if it was already open when we started
    If wasntAlreadyOpen Then
        newBook.Close
    End If

    Application.ScreenUpdating = True 're-enable screen updates
End Sub