You should be able to co-mingle a Sitefinity installation with your existing web site.
Sitefinity will serve pages that are setup inside it, otherwise the requests will be passed to the standard ASPX pages setup in the file system.
Here is what I would recommend:
1. Backup EVERYTHING (database & files)
2. Download the Sitefinity Blank Project Zip file.
3. Unzip the Sitefinity Blank Project into your web site's directory.
4. Access ~/Sitefinity and setup Sitefinity & your connection to your database.
At this point your existing web site should still work. Although you might need to re-do some of your changes to the web.config file. This file would've been overwritten by the unzipping the Sitefinity Blank project.
Now just setup your Sitefinity blog and create a Sitefinity blog page. You can link your existing ASPX pages to this virtual Sitefinity page.
In theory, this should work. Be sure to make good backups though.