Alpha witrh WarBRD base should work, many use it (me too).
So, what do you mean by "Elite does not see my stick"?
When you are in the bindings menu, you select one of the binds and then twiddle the part of the stick you want to bind, what is happening?
Oh, and regarding the power supply issues mentioned above by
@STRONTIUM DOG - definitely check this. The Virpil/WarBRD are a bit power hungry. Did you set up (in the Virpil utility) the LEDs to light up, and do they light up when you're running ED?