The OP kind of deflected the idea of Call of Cthulhu in his opening post, because Silent Hill is not about going mad (according to him).
Here is why he is wrong:
The Silent Hill games have always been about trying to drive the player mad. It is all about madness. You may not have noticed it while you were playing the games, but there are many fine details and deliberate design choices in Silent Hill that are meant to put the player in a certain state of madness.
So if you aim to bring that same experience to your table, then you are not going to achieve that goal unless you include that element of madness. Bringing a game like Silent Hill to life as a role playing game, is all about first understanding the subject matter.
Actually, being a big Silent Hill fan myself I would argue that the default state of every protagonist (and trapped member of the town) is madness. It's not about the journey, it's about what happens after you've arrived, so to speak*....especially in Silent Hill 2 and some of the others where the ultimate goal for a "best ending" might involve a modest amount of redemption and possibly an out to return to sanity.
On the OP, the only system I've ever really felt worked well for Silent Hill was Kult: Beyond the Veil (or its prior editions) but that amazingly cool and obscure system is OOP and hard to find for cheap, so my follow-ups would be to use any system with robust range of support for madness, body horror, mortality, blurring of dream and reality, and a big plus if it delves into very strange gnosticism. I'd be able to pull off a Silent Hill game using Call of Cthulhu, Chill 3rd, GURPS Horror or BRP but they'd all require some work. I also love Unknown Armies but the core principles of that setting really don't mesh well at all with the Silent Hill cosmology.
Kult, ironically, would give you all you need....sigh. I miss that game.
EDIT: Oh I'd also think Fear Itself is a good choice.
*For the player of a Silent Hill game it's about slowly figuring out just what horrible thing your protagonist did to get himself into his own purgatory, while also piecing together how all the other "inmates" relate to your guy's scenario, or what they did to get stuck in Silent Hill as well.