No contact

I have a 2006 Buick Ranier with the 5.3 engine. I recently had the battery replaced and now the car has developed a condition that when you turn the key to start, you get nothing no click as if something is not making contact. I have double checked battery connections and they are good. All other electrical works lights etc. This does not happen all the time. If you turn the key slowly it appears not to happen, dealer said if he does not see condition I am pretty much going to have to wait for total failure. Rather not if possible