you would need to install the 2015 and 2016 desktop apps for that. however, for 2015 and 2016 updates are no longer available. the cd's for those years probably contain the beta version which is not the filing version of the appp. you will likely change the .tax 201X files from what was actually submitted to some other state. even manually re-entering all the data won't help because the app is an earlier version than what you used to file.
your best bet is to print out copies of those returns or save them as PDF's. also, keep an offline copy. hard drives go bad and since TT does not have a copy of returns prepared on your desktop, the returns would be unrecoverable. the IRS only keep the last 7 years so at some point you wouldn't even be able to get a copy from them.
there is one other possibility. certain web services say they can open and print out copies of prior year returns after yo send them the .tax2xxx file. I can not vouch for them.
don't know what your new computer is but it may be possible to move the hard drive containing the apps and .tax201X files to the new one and create a dual boot computer. note that 2015 and 2016 were probably done using windows 7 which as time goes by with no security updates leaves your computer system vulnerable to hackers and malware.
TT usually makes the CDs for a tax year in November or December of the preceding year with whatever changes are known. before the filing date in the following January, there are usually dozens and sometimes many more updates - to correct bugs, calculations and update forms.
