I'm having the same experience on an upgrade from 4.0.2 to 4.3.5.
Connection strings copied and pasted from the old web.config ... they are correct. Credentials good - can log on with QA. User has db_owner role.
but no soup for me ...
file system has been upgraded, but not database; I"m still at 4.0.2 which makes sense, since it couldn't connect.
Can I run the database upgrade files separately?
Hmm ... well, I started to do so. Since I'm at 4.0.2, I started with 4.0.3 ... part of it ran ok, and then it tried to update this table: ProfilePropertyDefinition
After that, nothing but errors. There is no such table - not in my 4.0.2 database, nor in my 3.11 database.
First mention of it I see (as I search the install files) is in 03.02.03SqlDataProvider, and it's selecting, not creating.