What I would do on the old computer, is copy the whole Turbo Tax folder that is under your Documents. That should be where the .tax files and pdf files are stored. 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 your return. 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.
See this article on how to move your tax return to another computer…….
https://ttlc.intuit.com/community/tax-data-file/help/how-do-i-move-my-tax-data-file-to-another-compu...
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). Enter some basic information, then go to the state tab and download the state program. Then try to open your existing return, go to FILE - OPEN
