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See Move to a new PC or Moving your profile folder - Thunderbird if your profile is okay and you just want to move it. Most users who find this article should read one of those articles instead.
See Importing folders and Moving address books between profiles if you just want to move your folders and address books to a new profile that you create using the profile manager. If you do that Thunderbird will automatically run the new account wizard the first time you use the new profile. You will have to add your accounts again, customize your settings, and download/install any add-ons again. When Thunderbird needs a password it will prompt you for it. Enter it and check the checkbox to save the password. Unless you are using an add-on such as Lightning or Message Notes Plus you probably don't need to worry about moving anything else, and don't need to read the rest of this article.
Sometimes when you have problems with Thunderbird and can't figure out what's wrong, it's easier to create a new profile and transfer any data you want to save, rather than keep trying to fix your existing profile. In that case, read the rest of this article.