Checking for duplicates in a List of Objects C#

I am looking for a really fast way to check for duplicates in a list of objects.

I was thinking of simply looping through the list and doing a manual comparison that way, but I thought that linq might provide a more elegant solution...

Suppose I have an object...

public class dupeCheckee
{
     public string checkThis { get; set; }
     public string checkThat { get; set; }

     dupeCheckee(string val, string val2)
     {
         checkThis = val;
         checkThat = val2;
     }
}

And I have a list of those objects

List<dupeCheckee> dupList = new List<dupeCheckee>();
dupList.Add(new dupeCheckee("test1", "value1"));
dupList.Add(new dupeCheckee("test2", "value1"));
dupList.Add(new dupeCheckee("test3", "value1"));
dupList.Add(new dupeCheckee("test1", "value1"));//dupe
dupList.Add(new dupeCheckee("test2", "value1"));//dupe... 
dupList.Add(new dupeCheckee("test4", "value1"));
dupList.Add(new dupeCheckee("test5", "value1"));
dupList.Add(new dupeCheckee("test1", "value2"));//not dupe

I need to find the dupes in that list. When I find it, I need to do some additional logic not necessarily removing them.

When I use linq some how my GroupBy is throwing an exception...

'System.Collections.Generic.List<dupeCheckee>' does not contain a definition for 'GroupBy' and no extension method 'GroupBy' accepting a first argument of type 'System.Collections.Generic.List<dupeCheckee>' could be found (are you missing a using directive or an assembly reference?)

Which is telling me that I am missing a library. I am having a hard time figuring out which one though.

Once I figure that out though, How would I essentially check for those two conditions... IE checkThis and checkThat both occur more than once?

UPDATE: What I came up with

This is the linq query that I came up with after doing quick