This error message is weird. It suggests that you are trying to login with a login ID of 0, which does not exist. I have not seen this error before.
If you have a production system that needs to be running again asap, you could either rollback to a previous backup or we could find time for you on short notice to have a look via remote call.
If you require assistance, please let us know.
If you updated on a test system or have time to troubleshoot, you could first try to clear your browser cache and then try again. You would also need to go into more detail about what is happening. Do you get this error during upgrade or when somebody opens the browser? Does the browser show an error after authentication or do you not get this far?
Upgrading between 3.5.2 and 3.9.4 skipped 3 feature releases. It should work, but I would personally upgrade in smaller increments, to reduce risk.