Some steps you have to follow as below:
1. You must use exact same version of Thunderbird , in source & destination computers. later you can upgrade/update Thunderbird version as to your choice.
2. (keep the backup/COPY of all TB-profiles)
** usually Thunderbird-profile(s) are in : "%APPDATA%\Thunderbird\Profiles\" that is usually located in : "C:\Users\<WindowsUserName>\AppData\Roaming\Thunderbird\Profiles\" inside that "Profiles" folder.
NOW PROCESS TO FOLOW
In destination computer
use a command-line like below, to start Thunderbird, to choose specific Thunderbird-profile: start windows "Command-Prompt":
"C:\Program Files\Mozilla Thunderbird\thunderbird.exe" -P
above command will show a Profile choosing window, select a profile , check if that is your earlier profile which you want-back or not, if not then exit TB, again start TB with above command, & select another profile.
when you will find the correct profile that you want to use & have all previous emails+settings, etc , then remember the profile name which you selected in profile-choosing window. exit TB.
start TB again using above shown commandline. this time select the correct profile , and also select this option "Use this profile as default profile",etc similar. once you do above step , then you don't have to start TB with a command-line anymore.