How to select the first row for each group in MySQL?

I based my answer on the title of your post only, as I don’t know C# and didn’t understand the given query. But in MySQL I suggest you try subselects. First get a set of primary keys of interesting columns then select data from those rows:

SELECT somecolumn, anothercolumn 
  FROM sometable 
 WHERE id IN (
               SELECT min(id) 
                 FROM sometable 
                GROUP BY somecolumn
             );