When you reboot it does a search for new hardware. It will detect the missing device and reinstall it and hopefully correct the error that was there. It may ask for drivers but hopefully it will detect the drivers already installed and use them. Have your disks handy in case. I have never used Windows ME so i cannot comment but i would definitly concider upgrading to Windows XP. With Vista on the horizon there maybe a few copies left on the shelves going cheaper than normal. hope you fix your problem.
Another possibility is a virus or spyware has got into your system and creating havoc. Try running spybot and ad-aware to see if it picks up anything.
Best of Luck Allen