I also encountered this same set of errors while setting up a fresh install with my remote host.
Bombed on ERROR 400, try to reinstall via install wizard URL, it appeared to upgrade from 4.4 to current version.... then I tried to hit the site and received the DOES NOT EXIST IN THE DATABASE ERROR. Tried to rerun installer again via URL and it stated it was on the current version.
This workaround seemed to work for me...
Possible workaround (USE WITH CAUTION - my install was fresh) and I'm new with DNN platform
1) Locate the Version SQL table and select all records to file.
2) Delete all records from Version table
3) Run upgrade URL: http://www.mydomain.com/DotNetNuke_2/Website/Install/Install.aspx?mode=upgrade
No guarantees here... but it got me going again.
NOTE: in the event this workaround is successful for anyone experiencing this issue - BE SURE TO UPDATE/CHANGE YOUR HOST AND ADMIN PASSWORDS MANUALLY, as you will be bypassing the initial configuration wizard with this workaround. If you do not manually update these passwords, you'll be left with default credentials.
~Cheers