So it was indeed that you misunderstood Godel's incompleteness theorem. Yes, I'm aware of it, and was even suspecting that was what you had misunderstood, but wanted to hear from you just in case it wasn't. Anyhow, the theorem says nothing about the laws of nature -- only that every (certain kind of mathematical system) will have a true statement that will be unprovable in that system. But there is no hint that one of the unprovable things might be a law of nature, and if it were you could simply prove it in a different mathematical system.
What science can't do is produce absolutely certain deductive proofs. This is because science does not start with axioms but rather tries to discover them by induction. I'd also note that the axioms of science implied by the scientific method (ie, that the universe's laws are consistent across time and space, and that the universe is objective rather than subjective) can't ever be proven either. Of course, axioms by their very nature can never be proven.
PS: If you were interested in Godel's Incompleteness Theorem, you may also be interested in Turing's Halting Problem.