To the best of my knowledge, as long as you don't break any of the WARRANTY VOID IF REMOVED OR DAMAGED stickers, you're allowed to open it up. (that said, I'd still see if you could get in a chat with Asus support and double check that that's allowed.) That said, this sounds like a bad keyboard; I've had lots of laptop keys die on me before, but never four at once. Make sure that those are the only keys affected, and then remove the key caps, check to see if anything has gotten under the key membranes or anything, or if any have been damaged.
With the way keyboards are designed, often times many keys will be on the same circuit (if you hold both Shifts, you probably can't type any of the keys between them because of this), and it's possible that all those keys are on the same circuit and that circuit is damaged, in which case you probably need a replacement for the top panel including the keyboard... which, at $99 last I checked, is pricey. (unless you can get just the keyboard alone? Amazon appears to have just that for 70 bucks... not much better.) You're probably gonna have to go for the warranty repair if there's no easily visible problem you could fix, unfortunately.
