Let's just look at TableOne, TableTwo, and TableFour   
Most of the condition in the "in where" in are already covered in the join  
And suggest you use join on for all  

    Select TableTwo.Column1, DatabaseTwo..
    from TableOne  
    inner join TableTwo  on TableOne.Column4 = TableTwo.Column4 
    inner join TableFour on TableOne.Column6 = TableFour.Column6         
    where 1 = 1
    --- Section 2
    and TableOne.Column6 in  (Select TableOne.Column6 
                                from TableOne, TableTwo, TableFour  
                                Where TableOne.Column4 = TableTwo.Column4  -- covered in base join 
                                and TableOne.Column6 = TableFour.Column6   -- covered in base join
                                and TableFour.Column16 >= @StartDate 
                                and TableFour.Column16 <  @EndDate )

Pretty sure this is the same query    
Not sure if it is faster but I doubt is is slower  
The query optimizer has a better chance of filtering early  

    Select TableTwo.Column1, DatabaseTwo..
    from TableOne  
    inner join TableTwo  on  TableOne.Column4 = TableTwo.Column4 
    inner join TableFour on  TableOne.Column6 = TableFour.Column6   
                         and TableFour.Column16 >= @StartDate 
                         and TableFour.Column16 <  @EndDate