Restarts and Google Error Message

I use Vista 32 bit, on a Dell 1525. My browser is Mozilla Firefox, and I use IGoogle as my Home Page (and gmail).

The problem is that my computer restarts on its own, after it's been unused for a while, and the desktop screen that comes up has a dialogue box titled "Connect to www.google.com" with this message:

"The server Google at Please log in to your Google Account requires a username and password."

The screen then shows both my username and my password, and if I select OK, things work fine.

Any ideas (1) why the restarting, and (2) why the Google message?

Thanks

Run an antivirus scan and then download and run malwarebytes.

http://www.malwarebytes.org/mbam.php

Initially, sounds like a case of the nasties.