There's no way to specify a StringComparer at the point where you try to get a value. If you think about it, "foo".GetHashCode() and "FOO".GetHashCode() are totally different so there's no reasonable way you could implement a case-insensitive get on a case-sensitive hash map.
You can, however, create a case-insensitive dictionary in the first place using:-
var comparer = StringComparer.OrdinalIgnoreCase;
var caseInsensitiveDictionary = new Dictionary<string, int>(comparer);
Or create a new case-insensitive dictionary with the contents of an existing case-sensitive dictionary (if you're sure there are no case collisions):-
var oldDictionary = ...;
var comparer = StringComparer.OrdinalIgnoreCase;
var newDictionary = new Dictionary<string, int>(oldDictionary, comparer);
This new dictionary then uses the GetHashCode() implementation on StringComparer.OrdinalIgnoreCase so comparer.GetHashCode("foo") and comparer.GetHashcode("FOO") give you the same value.
Alternately, if there are only a few elements in the dictionary, and/or you only need to lookup once or twice, you can treat the original dictionary as an IEnumerable<KeyValuePair<TKey, TValue>> and just iterate over it:-
var myKey = ...;
var myDictionary = ...;
var comparer = StringComparer.OrdinalIgnoreCase;
var value = myDictionary.FirstOrDefault(x => String.Equals(x.Key, myKey, comparer)).Value;
Or if you prefer, without the LINQ:-
var myKey = ...;
var myDictionary = ...;
var comparer = StringComparer.OrdinalIgnoreCase;
int? value;
foreach (var element in myDictionary)
{
if (String.Equals(element.Key, myKey, comparer))
{
value = element.Value;
break;
}
}
This saves you the cost of creating a new data structure, but in return the cost of a lookup is O(n) instead of O(1).