Did you buy the 2019 CD or need to buy 2019? You can buy the download here, https://turbotax.intuit.com/personal-taxes/cd-download/
or if you have the CD you can download it instead.
How to download Turbo Tax instead of using the CD
https://ttlc.intuit.com/community/installing/help/i-bought-the-cd-but-my-computer-doesn-t-have-a-cd-...
Why do you need to install the prior years? Didn't you save the pdf files? 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.
