I would not recommend upgrading over the live site until you have done exactly that in a test environment.
Copy all website files from the DNN root down into another location.
Back up the database, then create a new database with a different name, and do a forced restore over the new database using the backup of the DNN database ... making sure you rename the files for the log and physical database to match those of the new database (important!).
Alter the web.config file to change the name of the database. Assuming you are creating the database on the same server as the original database, everything else - user permissions, etc - will be in place, so same user as is already in your web.config file has correct permissions.
Create a virtual directory in IIS to point at your new DNN site.
Now you should have two separate DNN sites, identical to each other. Fire up the new site and deal with any loose ends or issues to get it working.
Follow the normal procedures for upgrading DNN using your test site. It's a bit more complex than upgrading from one DNN 3 version to another - plenty of resource out there. Take good clear notes as you go, especially any problems encountered and their solutions. Don't rely on memory.
Once you successfully get it upgraded, test thoroughly.
You have not yet touched your production instance, either filessystem or database, except to copy each.
Before doing your actual upgrade, copy the filesystem and back up the database again, as you did before, just in case your upgrade fails.
If it does, replace the filesystem in its entirety with the backup, and restore the database backup to the database.
This is kind of a sloppy description, but you get the idea - do everything in a test environment first, and do nothing that will effect either your original filesystem or database unless you have the means to restore each to its previous state.