Going back to 2015

The software for 2015 and 2016 is no longer supported.  You cannot get updates for it and you would be unlikely to get accurate results if you try to use it.  And...as you already know, refunds for those years have been forfeited.  If tax is owed--it still must be paid.  You could get the paper forms and prepare them by hand.

2015

Form 1040  https://www.irs.gov/pub/irs-prior/f1040--2015.pdf

Form1040 Instructions  https://www.irs.gov/pub/irs-prior/i1040gi--2015.pdf

Form1040A  https://www.irs.gov/pub/irs-prior/f1040a--2015.pdf

Form 1040A Instructions  https://www.irs.gov/pub/irs-prior/i1040a--2015.pdf

Form 1040EZ   https://www.irs.gov/pub/irs-prior/f1040ez--2015.pdf

Form 1040EZ Instructions  https://www.irs.gov/pub/irs-prior/i1040ez--2015.pdf

2016

Form 1040  https://www.irs.gov/pub/irs-prior/f1040--2016.pdf

Form 1040 Instructions https://www.irs.gov/pub/irs-prior/i1040gi--2016.pdf

Form 1040A https://www.irs.gov/pub/irs-pdf/f1040a.pdf

Form 1040AInstructions https://www.irs.gov/pub/irs-prior/i1040a--2016.pdf

Form1040EZ https://www.irs.gov/pub/irs-prior/f1040ez--2015.pdf

Form1040EZ Instructions  https://www.irs.gov/pub/irs-pdf/i1040ez.pdf

https://www.irs.gov/filing/where-to-file-paper-tax-returns-with-or-without-a-payment

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

https://ttlc.intuit.com/questions/1901670-how-do-i-contact-my-state-department-of-revenue

Online preparation and e-filing for 2017, 2018 and 2019 is permanently closed.

To file a return for a prior tax year

If you need to prepare a return for 2017, 2018, or 2019 you can purchase and download desktop software to do it, then print, sign,  and mail the return(s)

https://turbotax.intuit.com/personal-taxes/past-years-products/

You may also want to explore purchasing the software from various retailers such as Amazon, Costco, Best Buy, Walmart, Sam’s, etc.

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

When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s.  Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS/state received the return.

Federal and state returns must be in separate envelopes and they are mailed to different addresses.  Read the mailing instructions that print with your tax return carefully so you mail them to the right addresses.

Note:  The desktop software you need to prepare the prior year return must be installed/downloaded to a full PC or Mac.  It cannot be used on a mobile device.

If you are getting a refund, there is not a penalty for filing past the deadline.  If you owe taxes, the interest/penalties will be calculated by the IRS based on how much you owe and when they receive your return and payment. The IRS will bill you for this; it will not be calculated by TurboTax.

https://www.irs.gov/filing/where-to-file-paper-tax-returns-with-or-without-a-payment

Doubt you will get the state programming for anything earlier than 2017 ... in fact surprised the federal update happened.    All you can do is get the forms & instructions  off the state website.