DOS game causes power off

I'm trying to run the old DOS game "Millennium" in a full-screen command box
under Windows ME on a new Asus motherboard (I'll have to open the machine to
get the model number) and have run into an oddity. When the game puts up a
pop-up menu, the machine powers off. In order to restore power it's
necessary to hold the power button in for about ten seconds, release it,
then press it again to get a power up. The machine is set up for "instant
off" on the power button. Windows is set up for, and does, turn the power
off on shutdown.

I've tried a few things in the DOS box setup (protection, don't let the
program see windows, fixed memory sizes) but none help, and some seem to
make it worse, such as disabling HMA causes it to turn the machine off as
soon as the game starts rather than waiting for a menu to appear.

I'd been assuming that the game was somehow hitting the registers which
powered off the machine, but I created a boot disk by hacking up an ME
startup disk and the game runs fine from there. Could still be, I suppose.
If I recall correctly, access to those registers has to be enabled. If
Windows didn't come up, perhaps access wasn't enabled.

Any ideas?

- Bill