It really depends on whether or not it's deemed a product "fault" or an end-user error. I'm guessing that as long as you didn't abuse your Powerbook, that it really is some hardware issue. In this case, I suggest you call Apple in lieu of going into a retail store. The rep will likely be more responsive to your needs, and you'll be able to explain that the broken hinge is really affecting your ability to use the machine properly. Best of luck
I take it the store clerk has activated/registered your MBP but you can check the status on the Apple site by typing in your MBP serial.
If it is not registered yet just register online with you APP code...it is very easy and you should receive a certificate by e-mail from Apple.
the coverage date should extend to three years from your date of purchase. if your applecare has not been activated, not to worry, because you still have until the listed date (one year from date of purchase) to activate the applecare.
apple will even bend on this rule if you ask nicely, which was the case with my girlfriend who never enrolled her rev A macbook's applecare since she got it in august 2006. i called them last week and they looked up the number and got her enrolled with no problem, even though it had been more than a year and she even lost her enrollment number