In general, you don't need monitor drivers.
Unfortunately, here in the UK, DSL modems, particularly the Sagems, cause all sorts of problems - Sudden reboots being a major one. Try a Google for your modem and see if any other users have had problems.
I'm surprised at the statement about no drivers being required. What make and model etc is this modem?
If you're using XP, entering shutdown -a in the Start>Run box will disable automatic shutdown on error.
Also, the Event Viewer may pinpoint something.