A new computer. Able to upload 2020 turbotax (from a CD), but cannot run it without the state taxes downloads. How can I get my previous purchased state tax downloads?

Start a fake 2020 tax return.  Enter your personal information which includes your state.  Then click on Online at the top of the desktop program screen and click on Download State.

I have changed a few computers. Since the CD that I bought include one state, I think that I was able to open my old returns.  I think that the state version will automatically downloaded.