Did you use the Online versions or the Desktop programs? If you used the Online version you can access them from any computer.
Your tax files end in .tax or .tax2015, .tax2016, .tax2017 or .tax2018 etc. They should be in your Documents in a Turbo Tax folder. You should also have the pdf files of each year. Or search your computer for all files ending in .tax. Also if you haven't done it, I would open each year in the program and save it as a PDF file, go to File-Save to PDF so you don't need the program installed to view or print your return in the future like to get a mortgage or loan, etc.
What I would do is just copy the whole Turbo Tax folder that is under your Documents. That should be where the .tax files and pdf files are stored. Copy that folder to a flash drive or best yet is to burn it to a CD or DVD and then you will have a backup of them. Then on the new computer copy the folder (or files) from the flash drive to your Documents folder.
The programs need to be installed from the CD or download them again. You don't need to install them unless you need to amend or open a return.
After you get the program installed the first thing to do before you open your tax return is to update the program and install any state programs you had. Then open your file. So you first might need to start a fake return to be able to download the state program (go to File-New Tax Return).
Then go to FILE -Open and find your return.
See this article on how to move your tax return to another computer…….
See this TurboTax support FAQ for moving the TurboTax files to another computer - https://ttlc.intuit.com/community/tax-data-file/help/how-do-i-move-my-tax-data-file-to-another-compu...
Any saved PDF of your tax returns can be opened, viewed and printed using any compatible PDF viewer program, such as Adobe Reader.
The TurboTax tax data files, which have a file extension of .taxyyyy, where yyyy is the tax year, eg .tax2018, can only be opened by the TurboTax desktop software for the tax year of the data file.
TurboTax prior year software can be installed on a Windows based PC using the Win-10 OS.
Depends on whether you used the Online software, or the Desktop software for those prior years.
1) IF you used the online software for those prior years, your upgrades is immaterial. You just have to pay for the software in each succeeding year to maintain access to the Online tax files (and use the exact-same Online account). Still, you should download and save your tax files in PDF format every year and save them off computer as a backup.
2) IF you used the desktop program every year, then you have to transfer the prior year files from your old computer to the new one. Before you get rid of the old computer, open each year you have installed and save each year's tax file two times to tow PDF files...once as a filing-copy....and a second time as the tax return, but with all forms and backup worksheets. Copy those to a USB, and transfer to your new computer. (save an extra USB copy and place in your bank safe-deposit box...or a fire-proof safe in your home). For 2016, 2017 and 2018, also save the final " .taxyyyy" data file and transfer to the new computer. You can re-install the 2016, 2017, and 2018 software on your new computer and work with those .taxyyyy datafiles (if needed to amend them for any reason). For 2015 and earlier, you cannot fully install those on the new computer, since you cannot get the proper update files, nor download any states you need anymore....thus the PDF files for those years are "CRITICAL" for you to create and save before you move to the new computer.