In your system BIOS, DISABLE Advanced Power Management (APM) or ACPI.
However, why would you want to do it this way? Saves you the trouble of manually having to switch off the computer every time.

I get only 'Please wait while your computer shuts down', and then it shuts off. My BIOS is CMOS Setup Utility.

You'll normally see that only on an AT class machine. ATX shuts off automatically.

Is an AT board rare? I cannot find any of it in eBay.

Probably disabling APM in System Properties control panel might help.
Windows 95 is not ACPI-capable, it can use only APM stuff in motherboard to switch power off. Even on modern mobos with ACPI.

AT boards are not rare, you have entered invalid search query. Use "socket 7", "486" keywords and almost all boards will be of AT type. Note that you need to change power supply, case and keyboard too. AT boards have a DIN-5 keyboard connector (not PS/2), one row but two-component PSU connector (not a single two row 20-pin like ATX's) and other screwing points (so AT boards cannot be installed into most ATX cases).

ATX is newer and has more features than AT, one of which is ACPI, or Advanced Configuration and Power Interface, which lets the OS shut down the computer automatically instead of you having to reach over and flip the switch like on an AT machine.

"It is now safe to turn off your computer" is NOT a feature. The absence of it IS a feature.

ATX style connector

AT style connecto

ATX came in around the same time as Pentium 2 So if your using a P2 or later then disabling power management like jesolo said in cmos will stop it turning off.

But it is a strange request, its usually a struggle to get Win9x to turn off by itself (windows bugs, nothing to do with hardware) and yours is actually working!

Some late Socket 7 machines used ATX as well.

oeuvre wrote:

Some late Socket 7 machines used ATX as well.

Some 486 have ATX-like power (but with different pinout), so it is why Windows 95, released before ATX was created, can manage power. 😀
But most of Socket 7 boards have only AT or combined AT/ATX power.