I would recommend that first you check that the td user and siteadmin user accounts exist within the new DB and are granted the correct roles and permissions (td should be public only and the siteadmin should be dbcreator, securityadmin, serveradmin, public, and sysadmin while installing/upgrading....note of using the SA account then sysadmin and public will suffice and more is not always good as in this case more permissions and roles will cause issues the same as not enough permissions and roles.). Then next I would suggest that you run the ownership queries from the installation guide that will change the owenership from the project schemas associated td account to the new DB's td account. You will also need to be using a local admin account on the application server to install so as to provide all the correct associated read/write permissions to the needed folders within the application server's operating system and make changes as needed. IF these are good you should then be able to install without error.
I have seen in the past where we had to delete the user accounts and recreate them on the DB and restore the project schema again as prior attempts to create the accounts resulted in residual permissions and issues that removal and recreation corrected.
Hope this helps,