I need to file 2013 Federal and NC returns. Can I do so on Turbotax?

No. TurboTax 2013 is no longer supported. Even if you find the CD version online and purchase it, you can not get the required corrections and updates needed. That means the return could end up being wrong, and since TurboTax only supports their software for three years back, they will not honor the 100% accuracy guarantee and you're on your own.

No.  Software for 2013 is no longer available or supported.  It is also too late to get a refund for  a 2013 tax return, but you can still file it.  You can get the forms from the IRS.

You can download the Forms and Instructions from the IRS web site:

https://www.irs.gov/forms-pubs

Remember to prepare your state return as well—if you live in a state that has a state income tax.