Hypothetically, assume that you have access to infinite computing power. Do we have designs for any brute-force algorithms that can find an AI capable of passing traditional tests (e.g. Turing, Chinese Room, MIST, etc.)?
What 'infinite' means here could possibly be debated at some length, but that notwithstanding, here are two conflicting answers:
'Yes': Simulate all possible universes. Stop when you get to one containing a flavor of intelligence that passes whatever test you have in mind. Steven Wolfram has suggested something broadly along these lines. Problem: the state of computational testing for intelligence e.g. Winograd schema would then be the bottleneck. In the limit, testing for intelligence requires intelligence and creativity on behalf of the questioner.
'No': It may be that, even with infinite ability to simulate, there may be some missing aspect of our simulation that is necessary for intelligence. For example, AFAIK quantum gravity (for which we lack an adequate theory) is involved in Penrose's "Quantum Microtubules" theory of consciousness (*). What if that was needed, but we didn't know how to include it in the simulation?
The reason for talking in terms of such incredibly costly computations as 'simulate all possible universes' (or at least a brain-sized portion of them) is to deliberately generalize away from the specifics of any techniques currently in vogue (DL, neuromorphic systems etc). The point is that we could be missing something essential for intelligence from any of these models and (as far as we know from our current theories of physical reality) only empirical evidence to the contrary would tell us otherwise.
(*) No-one knows if consciousness is required for Strong AI, and physics can't distinguish a conscious entity from a Zombie.
We're definitely nowhere near that level of AI; at best, high-tech solutions like deep convolutional neural nets can help with image recognition and some other algorithms can perform things like robotic movement adequately enough to be useful in some scenarios. None of this is even as sophisticated as the behavior of a flea, but no one refers to insects as "intelligent." It's exciting stuff that allows us to solve problems that human intelligence often has difficulty with (such as classification of thousands of objects, which would tire an ordinary human mind), but it's nowhere close to replicating our higher brain functions.
Also keep in mind that the Turing test is a poor test of "intelligence" that defies common sense. By the same extension, mistaking a mannequin for a human being in the dark does not mean that the mannequin is actually human. If it were a valid test, then we passed that way back around 1980 with programs like Dear Eliza which were coded in BASIC to regurgitate human speech patterns. There's just no need to come up with a sophisticated argument like Searle's Chinese Room to debunk it, since it's silly on its face; any layman should be able to see right through the Turing Test. If anyone except Turing had come up with this test it would not have received much attention. Turing displayed one-of-a-kind genius when it came to things like computing and cryptography, but like many other experts in such fields, he had a lot of trouble grappling with metaphysics and philosophy. Searle had more common sense, but his Chinese Room example is more of a rebuttal to the Turing Test than a test in and of itself.
What "intelligence" consists of is ultimately a deep metaphysical question, not a material one. For millennia, trained philosophers have had a lot of trouble assigning clear definitions to concepts like intelligence and consciousness. Until we can answer those questions definitively, using different sets of reasoning skills than scientists, mathematicians and computer specialists are used to employing (just look at how often metaphysics is derided in some of these disciplines) then we cannot say that we have achieved genuine A.I. Until we can define what intelligence is, we cannot say whether or not we've successfully built it; we've not only got the cart before the horse, but have yet to build the cart or see a horse. By the common definitions used in everyday speech we're nowhere near genuine A.I. No one calls cows or sparrows "intelligent," but our AI today isn't even as sophisticated as the mosquitoes that bite them.
That's not going to be a popular answer - I'll probably get a dozen downvotes for this, without anyone being able to adequately rebut my contentions, but it needs to be said. There's far too much irrational exuberance and gross overestimation of what we've achieved to date and probably always will be in this field. Historically, researchers in every generation have also grossly underestimated the computing power of the human brain; every decade or so, the estimates of the FLOPS and megabytes have to be drastically revised. We have a poor track record of even getting basic material questions about the human brain right. This clear, consistent pattern of biased overestimation of our success and the lack of any real definition, let alone a test, of intelligence is going to be a serious issue in this forum for its whole existence (assuming it survives the private beta period). We have a whole forum dedicated to a field we can't even define; we can't say for sure what A.I. really is, but we're adamantly certain that we're close to achieving it...! We cannot say if "brute force algorithms" exist when we're still groping for an understanding of what it is we're trying to force our way into. Certainly, there are brute force methods to solve certain problems, like Deep Blue does at chess - but we cannot say if that qualifies as intelligence or not. It is really not possible to answer questions like this without getting into deep discussions that immediately lend themselves to opinion and debate, which the Turing Test and Searle's Room are clear examples of, in and of themselves. Since implementation details of AI are considered by many to be off-limits here, we're limited mainly to highly speculative posts about tech that often doesn't even work yet (like Google's self-driving cars) and questions like this that we can't answer without first defining intelligence. This is going to be the root of a lot of problems here for a long, long time to come...
Infinite computational power in the absence of training data implies nothing beyond the ability to solve equations. In order to implement a behavior, criteria of success and failure are essential. A small bootstrap loss function with an adaptive feedback loop allowing its elaboration, infinite training data, and AIXI or Solomonoff induction would suffice, in principle, given your premise of infinite computational power. In fact, it would occur precisely as fast as the input data rate permitted. In practice, such general approaches require exponential time and space, and are thus intrinsically quite limited in application, absent some kind of efficiency hack. (Where 'efficiency hack' probably encompasses entire sciences, industries, and generations of research, and the resulting adaptation doesn't look much like, e.g., AIXI at all, in the end.)