Can I start TurboTax Online 2020 now that Turbotax no longer supports Windows 7.

The TurboTax online editions for tax year 2020 will not be available until early December.

Go to this TurboTax website to request a refund for the software purchased from TurboTax - https://support.turbotax.intuit.com/forms/refund-request.jsp
Use this TurboTax website to check your orders and payments -
https://turbotax.intuit.com/personal-taxes/cd-download/order-status/

If you can't  install Turbo Tax Desktop program you can transfer from your 2019 return from your computer into the online version when it opens in December.  You need to have the file ending in.tax2019 on your computer.

If you used the Desktop program last year here’s How to transfer into the Online version, expand the blue link if you used the CD/download last year (it hasn't been updated with the new dates yet)

https://ttlc.intuit.com/community/entering-importing/help/how-do-i-transfer-last-year-s-return-into-turbotax-online/00/25953

If you used the Desktop program before you may notice several differences and 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 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.