The problem is that your theme is calling on the plugin you deactivated. However, since that plugin is gone, the site displays an error and then stops rendering the rest of the page.

Here’s what to do:

1. Go to your WordPress administration. Click “Design” (or “Presentation”), then click “Theme Editor”.

2. Where on your site did the error appear? If it was on your sidebar, click “Sidebar.” If it was only on a search page, click “Search Template.” If it was in the comments section, click “Comments,” etc.

3. Now look for a function call that might be related to the plugin you just deactivated. For example, if you deactivated the Related Posts plugin, you might see some code like this:
   <?php related_posts(); ?>

4. If you don’t plan on using the plugin again, and if you’re sure the code belongs to the deactivated plugin, just delete the code.

   Or instead, you can follow these instructions to alter the plugin function call so that it won’t break your blog when the plugin is deactivated.

   (If you’re new to theme editing, you might want to backup your theme first just in case.)

5. When you’re done, click the “Save” button to save your changes.

6. If you couldn’t find any relevant code, or if the problem still isn’t fixed, repeat steps 3-5 for the rest of your theme files.

If all else fails, reactivate the plugin to get rid of the error, and then consult the plugin’s documentation, contact the plugin author, or file a support request at the WordPress Support Forums.

Here are two ways to do it:

The Quick Method

You can easily backup a single theme file by going to “Appearance > Editor,” clicking the file, and then copying-and-pasting the contents of the theme file you’re editing into a Notepad document. Read more detailed steps here.

The Complete Method

These steps will help you backup your entire theme:

1. Download an FTP program (such as FileZilla) if you don’t have one already.
2. While you’re waiting for that, go to your WordPress admin, and then click on “Appearance.”
3. Under the “Current Theme” header, note the file path that comes after “All of this theme’s files are located in.”
4. Once your FTP program is downloaded, installed, and ready to go, connect to your website by entering in your FTP hostname, username, and password (these should be different from your WordPress username and password). If you don’t know what they are, ask your web host for help.
5. Once you’ve connected to your website, browse to the folder that contains your WordPress installation (again, ask your web host if you need help finding it), and then browse to the folder you noted in step 3.
6. Tell the FTP program to download the entire theme folder to a location on your computer.
7. Once that’s done, check to make sure the FTP program says the files transferred correctly.