Hi Nick,
I can tell right away what is the problem. You are using Joomla! 1.5.8. As I have written in the documentation, you MUST have Joomla! 1.5.10 for Akeeba Backup to install properly. Older versions, up to and including 1.5.9, do not create Akeeba Backup's tables correctly and cause the error you witnessed.
HOWEVER! Your backup is complete. The only part which did not work is updating the database table where Akeeba Backup stores a detailed record of all backup attempts. You can find your full site backup at administrator/components/com_akeeba/backup and, yes, you can use it to fully restore your site.
The next step you must do is upgrade Joomla! to 1.5.23. Between 1.5.8 and 1.5.23 there have been over two years of development and more than a hundred bug fixes (among which, over a dozen SECURITY bug fixes). This means that your site is like having a neon sign reading "please hack me" over it. Upgrade in order not to get hacked. If the update fails, you can restore your site with the backup archive you have now. After you upgrade Joomla!, you can simply re-install Akeeba Backup and enjoy easy backups of your site.
As I have written many times, Akeeba Backup doesn't make full site backups possible, it makes them easier. You can always copy all your site files by FTP and take a dump of your database using phpMyAdmin (unless the database is very big, in which case you have to take a phpMyAdmin database dump of each one table at a time). Restoring this backup involves re-uploading those files, except the cache files and restoring the database dump. Of course, if it's a big database dump, phpMyAdmin will fail and you will have to edit the dump file, split it to several smaller files and restore one of them at a time. At the end of the process you will have to empty your session table and edit your configuration.php file manually. Time to backup: 1-4 hours, depending on site size. Time to restore: 2-10 hours, depending on the site size. And you have to spend that time every time you need to backup your site. Skill level required: medium high.
With Akeeba Backup you just install it and click on the Backup Now button. If it doesn't work, you'll spend a couple of hours with our support forum and fine-tuning the settings. From that point onwards, it's just 30 seconds up to an hour of doing nothing at all. Creating a CRON job takes 10 minutes to an hour (depending on skill level) and automates the backup taking process. So, potentially, you have to spend 0 time backing up your site. Restoring is also trivial using Kickstart and takes around 5-15 minutes. Skill level required: novice to medium.
So, it's your choice. If you want to spend hours upon hours doing manual backups, yes, it's an option. It does work, but it requires a lot of time and is an involving process. Because of that, you'll end up not having regular backups. And this sounds fine, until the day you'd wish you had twice daily backups. How do you think I ended up writing backup software for Joomla!? ;)
Nicholas K. Dionysopoulos
Lead Developer and Director
π¬π·Greek: native π¬π§English: excellent π«π·French: basic β’ π My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!