It does not sound as if you have previously used Moodle to change to unicode.
I would go back to your Moodle v1.7.2 installation and use the tool included to perform the unicode migration. This should change the entire database to unicode. (It is worth checking over the database afterwards though.)
To get your previous installation to work you will need to:
1. Make a copy of your config.php file
2. Rename current database (you will probably want to delete this later, but better to be safe and keep it right now)
3. Rename current Moodle v1.8 folder (don't delete as you will need this when you upgrade)
4. Restore old database. Check that the name of the database is correct - cPanel sometimes gives restored databases interesting names. Check also that a database user exists that has admin rights over the database. This user needs to have the same name as the one mentioned in your config.php file.
5. Install v1.7.2 files into your normal Moodle folder
6. Check/edit and then copy config.php into moodle folder
Once installed you will need to run the unicode migration utility and wait... (it can take a long time).
Once complete you will need to:
1. Check the database to see if it is all utf8_unicode_ci. I had to change a few of my tables.
2. Make a backup of the migrated database.
3. Rename your v1.7.2 folder (don't delete it - you may need it again if things don't work out!)
4. Rename your v1.8 folder to your normal Moodle folder.
5. Check/edit and then copy config.php into moodle folder
Best of luck!