For installation and software issues you can contact the TurboTax Support Phone Number
The program download and the license code should be in your Online account so you can download it again. See screen shot. You also will need your tax return file ending in .tax2024 etc. It should be in your Documents in a Turbo Tax folder or search your computer for all files ending in .tax.
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.
You only need the tax return data file ending in .tax2023 to transfer into 2024 or .tax2024 to transfer into next year. You can't transfer the programs. They have to be installed from the CD or Download. You don't need to install older programs unless you need to amend or you didn't save the pdf file. And they only support the last 3 years. If you install an older year you won't be able to update it or download any state programs, so you won't be able to open your return.
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-computer/00/26128