Can I can use TurboTax On-Line for 2020 if I have used TT CDs in the past (our computer will not support the new TT software version)?

[VolvoGirl]

Yes.  There is a way to transfer the .tax2019 file on your computer to the Online version.  Here's the instructions on how.  Expand the blue link if you used the CD/download last year. You will need to have the filed ending in .tax2019 on your computer. Transferring from last year will clear out anything you have entered for 2020 and you will have to start over.
https://ttlc.intuit.com/community/entering-importing/help/how-do-i-transfer-last-year-s-return-into-...

FYI,  If you used the Desktop program before you may not like the online version. It has less features and no Forms Mode. You can only do 1 return. Your return is only saved online so be sure to save both the .tax2020 data file and the pdf file to your computer when you are done. In case you need to amend it in the future or if you need a copy to get a loan or something. You might not be able to access your online return when you need a copy.

[macuser_22]

Yes you can but be aware that online only support s single tax return per online account and does not have all the features (such as the forms mode, what-if and other features) that are only in the desktop versions.