The best way is these simple steps: here is the info in brief steps:

1. ensure thunderbird is not running on old machine
2. enter %appdata% in search window on task bar and press Enter key
3. this should open windows file explorer in Appdata\roaming folder
4. highlight the Thunderbird folder and copy to external media
5. ensure thunderbird is installed on second computer and NOT running
6. enter %appdata% in search window on task bar and press Enter key
7. you should be in Appdata\roaming folder , copy&paste the exported Thunderbird folder there. This may prompt to overwrite an existing folder of same name. allow it
8. start thunderbird and all should be there

The above assumes Windows and that you use the default installation location

There is another way if your profile doesn't exceed 2gb: - click tools>export on old PC - click tools>import>import from a file on new PC (The passwords will not be transported in the process, unlike the above example)

Thanks for the reply. I'm not sure if the solution you have suggested will work in my situation. My old computer died and when they did the data transfer to the new computer the Thunderbird data was not there. I was told that this was a problem with Thunderbird.

No, that is not a Thunderbird problem, as all Thunderbird files are just that, files. Nothing unusual. Copying the profile folder is a guaranteed way to have thunderbird work as anticipated. If there is a problem, it is in the copying. Many proprietary copy programs attempt to optimize the transfer process and, in doing so, corrupt the profile. If the old computer boots, I suggest trying again. Or, if the hard drive can be accessed, the profile can be copied. I think what you're really asking here is "I have a profile that doesn't work. How do I fix it?" If that is the situation, then posting a screenshot of whatever Thunderbird data you have may help. On the default WIndows configuration, the profile is at c:\users\<yourid>\appdata\roaming\thunderbird\profiles\<profile name>. Ideally, users who copy the thunderbird profile have everything needed on new PC. Screenshots of the profile folder, plus of the imapmail folder within the profile and the Mail folder also will be helpful.

Thanks again David. Using your directions I was able to find the missing folders/profile data. I will direct the people helping me to the path you outlined above.

Ok, setting it up is easy, but only if you know how. Let me know if they have problems. The steps I posted do not work if all you have is the profile itself. If you found the thunderbird folder, that is a big help.