On the old machine:
1. Stopped the SEPM and IIS services.
2. Went to the SQL Management Studio and disconnected/detached the database.
3. Created a shared folder to the target server and copied ALL of the contents of the SEPM db path. Just to be sure. I know that it isn't necessary to copy the log files.
4. Then on the new server. Opened the SQL Management Studio and attached the db.
5. Re-configured the SEPM to use the database.
6. On the old one, we also configured it to use the new database. Although I could just reattach the old db just the same.
And the attaching and reconfiguring of the database for use by SEPM takes a bit of time. Usually over 30 minutes. So make sure you have patience. I left mine at home when I first posted this.
But then again, the old server has hung up on us quite a number of times already. So I really can't tell.