Step one, before doing anything else make sure SSL is actually working on your domain at all.
Do this by typing in your web browser...
https://www.yourdomain.com/..and hitting enter, your page should open with the lock icon in your address bar. If it doesn't, your problem isn't in Cube Cart, it's in your SSL on your domain.
There is a problem that will particularly affect many people who are on hosted or shared servers using cPanel (which is a vast majority of most everyone) to install their own SSL certificates from within the cPanel control panel, or if they are doing it manualy with OpenSSL commands from a shell and have cPanel installed.
cPanel will seem like it has worked to install your final signed certificate, but it will not actually always or if ever work. Depending on your level of access to the server your domain is on you'll have to go back in and physically move the certificate specific files and keys into the correct directory, then restart Apache on the server. This often requires access many people do not have on standard hosting plans so you'll likely find you'll need to contact your host providers support to fix it for you.
No need to worry, if this is a problem for you, as long as you were able to create your csr file and get your actual certificate back from your CA like it sounds you have, then it's just a matter of getting these files all moved into the correct directory. On most (just general, it could be anywhere, this is just a typical default) this directory is usualy
/home/ssl/certs/
Which should contain your
.csr file you generated, and your
.crt file your CA sent back to you.
/home/ssl/private/
should contain your
.key private key file, you can ftp to your domain and check that these files are actually in there, if not you'll need to find them on your server and move them to the right place manually, then restart Apache if you have access and it should work.
The above directory paths should hold true if your web pages are located in
/home/public_html/
Again, this is only if your initial test of checking http
s://www.yourdomain.com/ doesn't work. Also note, these instructions are general, not specific, since you didn't provide any info on your site or what it's running on the ability to provide you with specific detailed info would be impossible. It should however be enough info to get you through figuring it out at least.