There are few places where programs commonly store their additional data. Songbird's directory containing its settings and some other files should be in one of these - you just have to copy it over to the same place on your new PC.
- %appdata% - actually an alias to Application Data\Roaming directory. Type
%appdata%in the Start menu search box and press Enter to open it. - Application Data\Local - go one level up from %appdata% and you'll find a directory called Local, that's it.
- Program Data - it's located in your system drive's root and can be hidden, type
C:\Program Datain the Start menu search box and press Enter to open it. This is a less common one, used for system-wide, user-independent data. - Application's directory - the folder where an app is installed, usually located in C:\Program Files (or C:\Program Files (x86) if it's a 32-bit program installed in a 64-bit OS). Sometimes overwriting this directory with the old one also copies all settings and data.
In the latter case remember that you'll have to move that folder to appropriate directory - Songbird is a 32-bit app, so it will probably be installed in Program Files (x86) on the new PC, but in Program Files on the old one.