I'm so glad I was sitting before I read this!!
What kind of processor do you have?
2x2.8ghz ... intel? Amd?
In my experience, 4gb just isn't enough for Server2008.. but, with that being said,
Is it backing up before shutting down? Antivirus scan?
take a picture of the the most recent System & Application logs.. just the page, not individual ones.. let's see what's going on when it shuts down!