I'm not sure if this will help, but here's a suggestion: Go to ~/Library and see if you have a Google folder. In my system, there is a GoogleSoftwareUpdate folder within. You might try trashing it, if you have it. I also have a Google Earth folder in ~/Library/Application Support. Take a look there as well.
EDIT: I just found a Google folder in /Library, and it also contains GoogleSoftwareUpdate. A good way to find everything Google (including hidden files and folders) is by using
EasyFind.
Did you attempt to just log in as you would if you were starting up or installing an application? I just had the same pop-up happen and logging in took care of it.