This does sound like a screensaver-related issue. Let's see if it is the simple thing I think it is.
1. Open the Control Panel in the Start Menu.
2. If you see about ten icons with a few links under each, choose "Appearance and Personalization" (click on it) and then click "Change screen saver" under "Personalization".
3. If you see a large number of icons (several dozen), find "Personalization" and click it. Then click "Screen Saver".
4. In the "Screen Saver Settings" window that appears, do you see the box next to "On resume, display login screen" checked? If so, uncheck it and click okay.
If that box is unchecked, let me know, and we'll keep digging.