[eluser]Crimp[/eluser]
You have to decide what things are worth in terms of doing the work yourself. I take it that this site is not actually a blog, unless you read/write the posts to flat files. If you want an actual blog, with comments, you have to run EE or others, or roll your own with CodeIgniter.
CodeIgniter is a development framework. Basically just a shorthand way of gaining some common functionality in a web application. In one of the video tutorials on the CI homepage, it is described how to author and set up a basic blog with comments in 20 minutes. It's possible to watch the video and reuse that code.
If you decide to go that route, it is easy to port your existing design to CI views (the HTML code of the pages) and run the entire site off a CI install. This is preferable. But you would have to learn something and that may be more or less painful depending on how much you already know.
CPanel is just a control panel for server administration. To determine if you can run CI on your existing server, you need to find out the OS and if PHP and, for example, MySQL is installed. If they are, there's nothing stopping you.
It would also be no problem to port an existing design to EE. You just copy and paste the HTML into weblog templates and insert some snippets for blog posts and comments. That route will give you the desired functionality out of the box.