This is a bug in Excel (that we cannot fix or change) that can occur when you have both a password-protected VBA add-in, such as the Solver add-in, and a COM add-in, such as Google Desktop or our Risk Solver Platform / Analytic Solver Platform add-in. See for example http://www.excelforum.com/excel-programming-vba-macros/749838-vba-password-prompt-after-excel-closes.html.
When you see the Solver password prompt, if you press and hold the ESC key to dismiss the dialog (over and over) it will go away after a few seconds.
There are web pages such as http://www.add-ins.com/password_problem.htm that recommend that you go into the Registry and change the COM add-in's LoadBehavior entry from 3 to 2, and this can make the Password prompt go away – but it also means that the COM add-in will not be loaded when you start Excel. So this is not a recommended fix.