I would look around and make sure there are not extra copies of web.config or user.config in sub folders such as the /Admin folder or /Secure folder or other folders.
You should use the Web.config file that shipped with this version of mojoPortal and re-apply any customizations. We don't ship a user.config in the package so that would never be overwritten during upgrades.
Then I would delete the log file, it will come back again when it logs more errors. It is very strange to see those database errors since your site is showing content it must be connecting to the database for most requests. After deleting the log I would browse around the pages that are working and then see if any new errors are logged and then try the things that are showing errors and see if there are any different error details than what you have posted.
You might also try commenting out the PageNotFoundHandler in the <modules> section of web.config and see if you get any different error since the files do exist.
You are using the .NET 4 package of mojoPortal and .NET 4 hosting right?
Other than that it is baffling and just leads me more to thinking there is some strange hosting configuration going on, though I'm not sure what it is.
Hope that helps,