I had this problem recently, It turned out that i had a leak in one of the spark plugs... i brought a new set and replaced them myslef and the problem has now been resolved.
This might not be the solution for you but its worth looking in to
The windscreen wipers should definetly work when you turn the key to the second position... instead of turning the key the whole way round and starting the engine. If your certain this doesnt work then maybe there is a fault?
I had the same problem, tried everything but nothing seemed help it! it was so frustrating. In the end i tried my chances at a land rover garage and they managaed to sort it, if your around the essex area i definetly recommened you pay Broadfields a visit they'll tell you what exactly is causing it for free or they'll do it for you, it wasn't too pricey. Good Luck