all they'll try at the Genius Bar is to revive it via software methods...maybe restore/re-update/other software tweaks. If it is physically defective, they will not fix it there. They have only minor hardware capabilites in-store...adding RAM, changing a hard drive, etc...no diagnostic benches or soldering stations. Thus, if they can't fix it via software, it is likely physically defective, and you will get a new computer on the spot. Like I said, if they are out of stock, you will have to wait for stock, ususally a couple of days. Just note your current serial number.
I can't imagine they would, but if they try to get you to leave it for a physical repair, whereby they want to send it off to a repair center, and make you wait for it, don't let them. Demand, nicely, a fresh computer. I am 99.9% sure it won't even come to that.