(In the following, excuse me if my english is not 100 % as I am, too, not a native english person. But that does not stop me from trying my best to write flawless english).
I've been pondering the exact same question for years, wondering if I could be the only brain in a vat with everybody else walking around (just an extreme example of solipsism (I am the only BIV)). Now, the Buddhist solution seems like "shoving all problems under the mat" and instead focusing on positive things. A very pragmatic survival strategy. But that does still not solve the problem/answer the question. Or does it......? Let us see.
Now, I've read "a lot" of Wittgenstein, and it just occured to me the similarities to Buddhism. From what I understand of Wittgenstein (there are of courrse numerous interpretations and camps, like for every other philosopher), he says that questions like these just tells us that something has gone wrong, our minds has been led astray into misconceptions that are pure and simple nonsensical (perhaps not pure and simple in an obvious way). And it's actually language with its concepts and ways to say things (syntactical constructs) that fools us into thinking that BIVs are important important questions, that they make sense at all. Instead, BIV is just a nonsensical quarry.
So we need therapy to get used to thinking normal again. The way to "be normal again" is e.g. to see how deep important philosophical questions just turns out to be nonsensical constructs, to teach the mind not to walk into a trap. For instance, "having a pain" and "having a car" - perhaps not the best example, but these two phrases or syntactical constructs share the same structure, yet pain is not something that you have in the same way that you have a car. Nobody would of course argue here, because it's so evident in this case. But something along the lines. Wittgenstein, I think, had numerous other strategies to show nonsensicality.
Now, how does Buddhism relate to Wittgenstein ? I am unsure, because I don't know much about Buddhism, but I think that both Buddhism and Wittgenstein can be said to claim something. And once you claim something, you can be attacked. But whilst Wittgenstein actually claims that there exists (even if only one) nonsensical constructs in our language that can be remedied by teaching ourself that such and such leads to nonsensicality, Buddhism (it seems) only says that you can free yourself of such torment as philosophical problems (which are nonsensical) by doing such and such (Buddhism takes no philosophical stand, it's more pragmatic) - but Buddhism still makes a claim, namely that you can actually free yourself of pain/torment by strenghtening such and such ways of thinking (focus on positive and harmless things) and weakening such and such ways of thinking (e.g. philosophical problems and paradoxes).
Now, the damnest thing happened to me in the process of writing this. I actually was starting off in the normal way, presenting views, then arguing against them, then presenting a better view. I don't think I even finished the first part, because it struck me that I should listen to what Buddhists have to say (I once thought Wittgenstein was crazy.....now I think otherwise). So, how do I relate to the world, the stuff that's around me, the objects that I sense, etc.. ? In order to not get killed, I surely will have to think that cars are real, otherwise they will run me over. So I will have to discern important from nonimportant things. Cars and your everyday life is important, philosphical problems are not. But can you teach your brain to be dual in this sense ? Once you start treating something as nonimportant (that we before thought was as important as e.g. cars) we run the risk of treating cars as less important as well. Soon you become detached mentally and end up in front of a car because you didn't react in the way you used to.
Ok, I could have continued but will stop since I wrote the above on purpose just to see how one might think. I don't think that what I said is any good etc. But what I wrote still illustrates one way of asking and thinking.
Now, give me feedback.