You know there's a bunch of schema changes between 4 and 3, right? :)
If you pointed RT4 software at the RT3 database, the upgrade process
changes the schema.
Well, yes; part of the process is running the upgrade scripts on the database,
which was done, and seemed to complete successfully. Essentially it was a new
install of RT4 into its own directory, as per instructions, giving it the rt3
db name, user, and password; the upgrade script was run against the RT3
database; then the Apache conf of the site was altered to make the RT hostname
point to the rt4 docroot instead of rt3. This seems to match the docs, yet
going to the site gets a 4.0.0 web page with "Hi! No database! Tee hee."