ditto his answer. CSB's tlx design file is a nice suitcase! Pack and travel with it conveniently.
But keeping proper copies is a MUST in case anything should happen to that because nothing can replace it.
You can use the PREVIEW function on your own new computer to have CSB "publish" your website files to your computer. In the publishing options, check the box to use a local HTML file and assign it to a folder in your my docs area. Then Preview. CSB will generate a copy of your website files, photos, the uploaded download files, etc. So your new computer will then have a copy of those files. Remember to UNCHECK that local HTML folder box before publishing to the web! Leaving it checked during publishing SOMETIMES removes files from the website!
Note that any file that was uploaded to your website OUTSIDE of CSB (with FTP or your site manager, etc) will not be in the CSB file and should be copied over from the old drive to the new one. CSB does not care where you had your old files because it does not go back to use them again.
The first time you try to publish your tlx design files from the new machine to your website, you will have to publish the WHOLE FILE. This may take quite some time, or several tries to get it complete, especially if your file is that big but once done, the file will publish only updates again.