The short answer is, "Ask a lawyer."
The longer answer is what others here have said - you're probably out of luck. Carfax is far from perfect (the biggest flaw is they rely on self-reporting), but it's better than nothing and there is literally no excuse to not get one. You put yourself in the hole 2k to buy this car but you didn't spend the extra 40 bucks? Never mind that any decent dealer should offer you that or an Autocheck for free in this day and age.
And of course, you can also get Autocheck for free anyway with this helpful hint.
Ultimately you have to prove the dealer misrepresented the damage and with nothing in writing you'll be stuck. If it's running well, just enjoy the car, pay it off and you'll do better next time.