I think there's two points to consider.

First is the request for your current salary. In several states it's actually illegal to ask that (I'm assuming you're not in one of those), but regardless, there's a polite way of saying that's not relevant if you don't want to disclose it. If this causes the company to back out, you probably dodged a bullet.

Second is the request for your desired salary. You should have done some research and had a ballpark figure to offer. At the very least, say something like, "I would like to earn something in the $X-Y range, but that's flexible depending on the benefits package." If you're not willing to even do this, the company likely dodged a bullet.