I just realized I glossed past the part about you not filing in 2013. Or rather, mailing them in but them claiming they didn’t receive them. I’ve never mailed in my taxes and our CPA handles everything at work so I have to ask, or rather, I assume, there’s no confirmation when you mail in your taxes, is that correct?
I’d still go ahead and call them and see what they have to say and go from there. You can probably tell them that you DID mail in your tax return and go from there. You may want to save a PDF to your computer and offer to e-mail it over the the agent on the phone right away so, at the very least, you know they have it now.
Do you have the money to pay what you owed at the time? (did you then*)? If you do, and you can make the payment right now, it may be worth it to ask them to waive the interest and late penalty if you make the payment right away. [If you can do it] they’ll probably be just as happy to be done with it, as you’ll be to not have to pay all the extra money. If you can’t, I’d ask them to wave at least the penalty and possibly start the interest as of now and get an installment plan set up. Then go look up some resources online and fine the paperwork to send in to see about getting the penalties waived, if you incur any. There are some ways around them for people that don’t do this often.
One last thing, what’s the status of your state return for that year? If everything is okay with that, that is, it’s filed, the payments were made or the refund was issued, you may want to have that ready to go before you call as well. It may also help to show the IRS agent that you did make file that year.
*Another thought, did you have enough money in your account back then? If not, that could have been the problem. If they were trying to pull the money and couldn’t, it might just be catching up with you now.
ETA, and as long as you’re not looking to get out of them, I wouldn’t sweat it too much yet. It’s entirely possible that you’ll call and it’ll be one of those ‘hey, no big deal, this happens all the time, just send them over and we’ll get it cleared up’ things. No matter how it turns out, the tax man isn’t going to be banging down your door any time soon.