M.F.
First, how did you cancel? By phone, email, website? Have you combed through your junk mail and trash folders around that date for a possible cancellation confirmation email? That's where I'd start.
Whenever I call customer service, ESPECIALLY when I want them to go out of their way to help me fix something I should have fixed earlier, I always start of with a polite, sweet "Hi, I'm hoping you can help me." If you come across to customer service that you're enlisting their help with a problem instead of coming across like you're ready for battle, you get much further.
If you are calm, sweet, a little self-deprecating ("I can't believe I didn't notice this x months ago!") and simply explain that you used the service in ______ of 2012, found a babysitter right away and, after paying for that month's use, cancelled your account. You used ______ method to cancel your account and haven't used the site since. You never received any emails from them after you completed the cancellation and thought it was all processed correctly. "I'm totally kicking myself that it's taken me so long to notice, but as I was preparing for my taxes I just realized that the $35 monthly fee has been auto-debiting from my account the whole time. Can you please help me?"
Once you pull out the threats, you loose any chance of actual help. They might not be able to refund your money, because you have nothing to prove you actually cancelled and it has been some time since you did, BUT if you approach them the right way, you might get some or all of your money back. Lesson learned, at least.
Good luck! :-)