Re: My samsung alpha touchscreen is totally unresponsive but the buttons work
If it's 4 days old, bring it back to the carrier (or store it was bought in) and ask them to exchange it for a new one that works. That's what warranties are for. We're not perfect yet, so some devices we make (like your screen) do fail, even very young. (Most warranties run around 15 days for replacement with a new one - during the holidays, some places extend that to 30 days. 4 or 5 days is certainly within everyone's limit. After that they'll replace it with a refurbished unit - which, as far as I'm concerned, is better. Some human being went over that unit to make sure it was working, not scratched or nicked, etc. A new unit was checked by a computer [and if it had the equivalent of your bad touch screen while it was checking a phone, something might have slipped through]. My year old Note 3 is a refurb - the first two new ones developed problems.)
As far as why the buttons work but the screen is unrespponsive, the buttons aren't part of the screen. It's like asking why your TV works but your porch light burned out. The screen and buttons are near one another, but they're not electrically part of the same thing.