If a user can start search without any text input, they need to receive some meaningful results. It can actually be a feature: maybe your user doesn’t know what to type in, but you think you have something to offer them anyway. Show them your hot offers, suggest something based on your knowledge about user.
There was a conception of “zen search” when you don’t type anything, but get some random results after clicking [Search].
This is not a direct answer to your question, but maybe it can solve your problem. Your button can be always available and always working. No need to disable it. Just show people something good.