In C# 3.0 you can use LINQ's Concat method to accomplish this easily:
int[] front = { 1, 2, 3, 4 };
int[] back = { 5, 6, 7, 8 };
int[] combined = front.Concat(back).ToArray();
In C# 2.0 you don't have such a direct way, but Array.Copy is probably the best solution:
int[] front = { 1, 2, 3, 4 };
int[] back = { 5, 6, 7, 8 };
int[] combined = new int[front.Length + back.Length];
Array.Copy(front, combined, front.Length);
Array.Copy(back, 0, combined, front.Length, back.Length);
This could easily be used to implement your own version of Concat.
You need to use reflection to get the method to start with, then "construct" it by supplying type arguments with MakeGenericMethod:
MethodInfo method = typeof(Sample).GetMethod(nameof(Sample.GenericMethod));
MethodInfo generic = method.MakeGenericMethod(myType);
generic.Invoke(this, null);
For a static method, pass null as the first argument to Invoke. That's nothing to do with generic methods - it's just normal reflection.
As noted, a lot of this is simpler as of C# 4 using dynamic - if you can use type inference, of course. It doesn't help in cases where type inference isn't available, such as the exact example in the question.
Best Solution
Why do you want to do that? If there's an error, log it in event log and throw an exception. Your service won't be started and the user will be informed that something bad happened.