The file /opt/picasa/bin/picasa is a bourne shell script.
Try to run it in verbose mode:
$ bash -vx /opt/picasa/bin/picasa
... a lot of commands finishing with....
# Then, actually run Picasa
exec "$PIC_BINDIR"/wrapper license.exe.so /gate Picasa2 "$*"
+ exec /opt/picasa/bin/wrapper license.exe.so /gate Picasa2 ''
As you can see above, the script ends by calling "/opt/picasa/bin/wrapper".
Try to run it in verbose mode and may be you see an error message somewhere.
Other alternatives are:
1) move $HOME/.picassa to $HOME/old.picassa and try to run picassa again
2) uninstall picassa, remove the /opt/picassa and re-install it