They still haven't addressed why the Silence want to build a TARDIS. They say they just want to kill The Doctor because he's dangerous, but if someone were trying to make their own TARDIS, bumping off the last of the Time Lords would probably be a smart move.
Or vice-versa. Do they want to take out the Doctor so no one will interfere with their getting a TARDIS, or do they want to build a TARDIS so they can more easily take out the Doctor?
I imagine both goals are somewhat complementary. They want the Doctor dead not just because he's generally dangerous but because he's dangerous to them in particular -- if he survives, Silence Will Fall. And they want a TARDIS because -- well, we don't know for sure, but c'mon, EVERYBODY wants a TARDIS. You don't really need a reason.
The question then is, if they're going to kill The Doctor, why not just take his TARDIS? This could have something to do with the TARDIS blowing up last season; perhaps the Silence tried to steal the TARDIS, but something went awry and it blew up, so they decided trying to make their own would be a safer option.
Speaking of the Silence, I don't believe anyone's mentioned this in this thread, but it's pretty clear that they're supposed to be the basis for the Men in Black stories, right?
Well, the entire history of Doctor Who is full of aliens and government coverups, at least on back to Troughton. The Silence are just one more entry in a long tradition. (I still love the idea that those 17 missing minutes in the Nixon tapes aren't actually missing, though.)
Well, the reason I went with MIBs is because, aside from the obvious(the fact that they all "dress" like MIBs), there's also the whole memory filter thing, which fits in pretty well with the MIB mythos: anyone who's ever seen them doesn't remember the experience, not because of red light flashy thingies, but because of whatever the Silence do to edit themselves out of their memory. It might not be perfect, though, and over time, perhaps enough invididuals had vague recollections of identical, shadowy figures in black suits that the MIB myth sprang from there.
I suppose it is possible that The Silence patterned themselves after the MIB myth, in order to insure themselves against failure of the memory editing thing. If someone DID manage to recall an encounter with them, and all they could say was that they saw a dude in a black suit, they'd just be dismissed as another crackpot conspiracy theorist.
Or it could be both, timey-wimey stuff and all that.