Your tax returns are stored in document files with names like "John Smith 2019.tax2019", 2018, 2017, etc. (although the filename extension may be hidden depending on your system settings.) When you use the desktop version of Turbotax, only you have the tax documents, they are not backed up with Turbotax, and you are responsible for your own backups and security.
To re-install Turbotax, you need access to the installers. If you bought the program on CD, re-install from the CD. If you bought a download, check with the vendor to see if you can download a new installer. Turbotax allows unlimited download attempts from your online account. Once you install the base program, you will need to update it and reinstall the state modules you used. They should also be accessible from your Tax account if you log into Turbotax online and go to your list of prior purchases. Turbotax only supports the program for three years, so you probably won't be able to reinstall or update 2016 and older.
You can get copies of older returns from the IRS.
https://www.irs.gov/individuals/get-transcript
If you saved your tax returns as PDFs (and not just as tax return documents) then of course the PDFs can be viewed on any computer with a PDF viewer program installed.
