You cannot actually copy the program over, as it relies on the registry and various files on your computer. Thus, if you want it on another computer you'd have to click here to download and install it on the respective system.
However, you can copy over the preferences, extensions, mail, etc manually. Since it appears you have Windows XP, you'll find your Firefox Profile in the directory C:\Documents and Settings\username\Application Data\Thunderbird\Profiles. After you install Thunderbird on the new drive, go to the above location and delete the folder random characters.default. (NOTES: The "Application Data folder is hidden by default, so you'll have to enable the viewing of hidden files and folders in Folder Options. Make sure Thunderbird is closed when you do this. ''Random characters'' is actually a series of random characters.) Then copy over the random characters.default folder from your old drive to the new one. Launch Thunderbird and all should be well.
Hope this helps,
I know that there are tools for backing up Thunderbird but I haven't found one that will back up from a location other than the default. I moved a bad hard drive to an external enclosure and connected it to another computer to recover files. Now I need to recover the Thunderbird files. Does anyone know where I find those files and which ones I would need to copy over to a new installation?