Best of luck getting your 3DS fixed. I wouldn't judge the guy for telling you it won't be covered by warranty, however. Warranty protects you against any manufacturing/production faults - the hinge breaking could either be this or more likely from user wear-and-tear. If you didn't buy the 3DS that long ago, and it's still within its warranty period, definitely highlight this though - as the quicker it's happened, the more likely it is to be a weak product, that could then be argued to have to be covered by warranty.
If the game was preloaded, it may be worth seeing if it was associated with your account upon signing in. Can't save data be loaded onto your SD card as well? I haven't used my 3DS in a long while...
After many years, I have decided to return to ACC, and I even donated $10.
I'm new to PC gaming and still love to play on my 3DS.