I need to access a Turbotax file from 2000 and/or 2001. I have the file but not the program. Can I access a TurboTax program from that time period?

So you have the .tax files?  

Only if you have the programs installed for those years and the state programs. But Turbo Tax only supports the last 3 years so even if you install an old program you won't be able to update it or download any state programs you need.

OR you could try the TaxPrinter service to convert a .tax file to pdf at
https://www.taxprinter.com

They might be expensive and it is probably not safe to email tax returns back and forth. They are not related to Turbo Tax. I don't know if they can do State.

Sorry, the TurboTax software for tax years prior to 2019 are no longer available.

If you need to print out those returns there is a service that will print the returns for you for a price.  It is not recommended by TurboTax -  https://www.taxprinter.com/

It's always a good idea to make a backup copy of your tax data file, in case your original gets lost or corrupted. Here's how:

1. From the File menu in the upper-left corner of TurboTax, choose Save As (Windows) or Save (Mac).
2. Browse to where you want to save your backup.
   • Tip: If you're saving to a portable device, save it to your computer first to prevent data corruption. Then, after completing Step 4, copy or move the backup file to your device.
3. In the File name field, enter a name that will distinguish it from the original tax file (for example, add "Backup" or "Copy" to the file name)
4. Click Save and then close TurboTax.
5. Restart TurboTax and open the backup copy to make sure it's not corrupted. If you get an error, delete the backup and repeat these steps.

If you make changes to your original tax return file, repeat these steps to ensure your original and backup copies are in-synch.

Related Information:                             

• Retrieve a Tax File from a Portable Device
• What's the difference between the tax data file and the PDF file?

AND save it as a PDF so you have access to a copy even if you don’t have the program still installed and operational :

• How do I save my return as a PDF in the TurboTax software for Mac?
• How do I save my return as a PDF in the TurboTax software for Windows?

AND protect the files :

• How can I protect the tax files on my computer?

yes they can do state for an additional fee. about $45 for federal $80 for federal and state. don't know if the fee is higher if there are multiple states. you do this at your own risk but sometimes you have no choice