I'm linking you to a TurboTax FAQ that includes instructions on moving your tax data file to your new computer.
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Are you on Windows? 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…….