Magento Upgrade Error :: “Table ‘core_variable’ already exists”

It is a dirty method and I am not advocating that it will work for you.

Rename the file(s) that show up in the error: (eg: mysql4-upgrade-0.8.18-0.8.19.php renamed to mysql4-upgrade-0.8.18-0.8.19.php-)

You may have to do this several times for each file that the next error will display. (To display errors, rename /errors/local.xml.sample to local.xml)
Eventually after renaming a few files, you will get your home and admin page to display.

Now that you are able to see your front and back end(s), login to your admin panel.
Re-index all data. Diasble and Flush cache.
Since you are already on 1.4.0.1, running (magento-core/Mage_All_Latest) from magento connect or ./pear install magento-core/Mage_All_Latest-stable (via SSH) will not work as it will say the latest is already installed.

So from Magento connect, Re-install: Mage_Core_Modules
It may re-install 1.3 instead. If that is the case, simply select upgrade to 1.4.0.1

That will take care of any files that were files you renamed (as mentioned above).
Finally to fix/update your toolbar layout (to 1.4) you have to to update the toolbar. You may also get a “Invalid mode for clean”
Both solutions and others can be found here: http://www.sonassi.com/knowledge-base/magento-1-4-install-errors/

PS: You can use the db repair tool to verify this with a clean 1.4 install.