How to Trouble shoot Windows 95 Shutdown Problems
By: Arie SlobView Microsoft's Knowledge Base Article No. 145926 for troubleshooting Windows 95 Shutdown Problems.
If you have Internet Explorer 4.x and/or Outlook 98 installed, see also this page: Windows 95 Shutdown problems
One possiblility when your computer stops responding (hangs) at the Please wait while your computer shuts down screen is an incompatibility between the Windows 95 Advanced Power Management (APM) system and the APM-capable BIOS in your computer. If the BIOS in your computer instructs the system to suspend, rather than shut down, Windows 95 cannot shut down correctly.
As a temporary workaround, disable APM support. To do so, double-click the Power icon in Control Panel, and set the Power Management setting to Off.
You can also contact your computer or motherboard manufacturer to inquire about a BIOS upgrade that resolves the problem.