Are you absolutely sure that computer is designed to shutdown - meaning power off - automatically? My Win 98SE computer is a 10 1/2 year old computer, originally a 75MHz Pentium with 8MB RAM and Win 95, later upgraded with an overdrive processor which boosted it to 200 MHz w/MMX, along with memory upgrades ending at 128MB and other upgrades. But, it, and most, if not all, computers of that vintage had to be turned off manually. I have the computer and the monitor connected to it plugged into a surge protector. I just leave power switches on the monitor and computer in the ON position and turn them on and off via the switch on the surge protector.
The shutdown screen you're talking about was merely a notification to the user that it's okay to turn the power off now.