I'm afraid I don't have any help--but I can confirm that I have a client with a similiar issue.  We've had Dell out to replace MB and hard drive--the issue has improved but not gone away.  About once a month, we get an unexpected shutdown.  

I did update the Broadcom Network drivers to the latest version after seeing them cause a shutdown once (blue screen).  That seemed to help but the problem is not gone away completely.  

We also sometimes get reboots.  Often, nothing shows up in the event logs until after the restart--then an "unexpected shutdown" is logged.

Any update? I have this problem too but the buzzing one when the monitor or computer is set to sleep is more widely known.

Our school district has 24 of these, and sadly ALL of them have gone down one way or another at least once. The most common problem is that someone will be working on something or walk away from the computer for say an hour, only to find the screen is off and the computer does not respond to keyboard, mouse, or power button presses even though the power button is still lit up a solid white. The only way to use the computer again is to either hold the power button until it kills the power, or pull the plug. We have tried changing all kinds of setting with power management; disable sleep, enable wake on mouse, disable dimming the display...etc. We have also tried updating the bios, as well as the video, network, and chipset drivers with no avail. We have been calling Dell everday for the last week, and all they have done is send a tech to replace the motherboard, heatsinks, and memory in one of them only to have them short out the lcd inverter. Although we can't confirm that this fixed the problem, we are very doubtful that 24 computers happen to have the same combination of faulty components.

If anyone can shed some light on this situation we would greatly appreciate it. From my research this problem seems to be common among the Inspiron One 2305's and no one seems to have found a fix, and Dell hasn't acknowledged the problem from what I've seen.