Assuming you are using Windows OS on both computers.

Make sure you install exactly the same version of Thunderbird on new computer as you are using on old computer.

On old computer:

• Exit Thunderbird
• In Windows search type: %Appdata% - see image as guide.
• select the %Appdata% file folder
• Select 'Roaming' folder
• Copy the 'Thunderbird' folder to an external drive.

On new computer:

• install same version of Thunderbird.
• Exit Thunderbird if it ran.
• In Windows search type: %Appdata%
• select the %Appdata% file folder
• Select 'Roaming' folder
• Delete the 'Thunderbird' folder
• Paste the copied 'Thunderbird' folder into the 'Roaming' folder thus replacing the one you deleted.
• Start Thunderbird.

I would advise - on new computer, access your Firewall and make sure Thunderbird is set up as an allowed program. You do not want the Firewall blocking access to the internet.