You might have better luck if you try installing the packages from the command line, which you would do by typing:
(Obviously, replace 'package-name' with the name of the .deb file.) If that fails and you're sure that you're using the package built for the right architecture, please post here all of the output that you get.
sudo dpkg --install package-name.deb
Also, as I recall, the 'Linux' version of Picasa is just the Windows version packaged up with wine, since Google apparently doesn't want to be bothered to compile a real native Linux version. So as an alternative to the above, you could basically install the same thing by first installing wine:
and then downloading the Windows .exe file for Picasa and opening it.
sudo apt-get install wine