NOTE: This is a bit verbose in the description, but maybe you can learn something from the process. If you just want to know how to fix the Banshee database after changing user-name or moving your library to a different location, scroll down.
I recently reinstalled Ubuntu and in the process changed my user-name to my more commonly used 'cybolic', however after copying the ~/.config/banshee-1 directory to my new home-dir, I realised that Banshee had all my music indexed by absolute path, meaning that it was looking for my old home-dir and so couldn't play any tracks.
To fix it I assumed I would have to do a search and replace on its database, but I needed the filetype, so a quick file ~/.config/banshee-1/banshee.db later I now knew that it was in SQLite 3.x format.
Now on to a tool to do the search and replace on the database...
Ubuntu has a tool in its repos called sqlitebrowser, that sounded about right, so I installed it and yes, it allowed me to browse the database and perform SQL queries - just what I needed.
So, long story short, to change the location of your music files in the Banshee database, here's what you do (close Banshee first):
sudo aptitude install sqlitebrowser
sqlitebrowser ~/.config/banshee-1/banshee.db
Now change to the tab labelled "Execute SQL" and write something like the following:
update CoreTracks set Uri = replace(Uri, '/home/<olduser>', '/home/<newuser>');
update PodcastEnclosures set LocalPath = replace(LocalPath, '/home/<olduser>', '/home/<newuser>');
You are now done and can start Banshee again :)