laptop

Does this happen while you are using them? If this is happening while your are actively using them, don't waste your time. There are issues you don't want to bother with.
Do the system get noisy before they shut down?

For both of these machines I would look at the APM (Advanced Power Management) settings. Depending on the version of Windows it may vary a little but eith er right click a blank area of the desktop, select properties then go to the Screen Saver tab. You will see the Energy Star logo in a box. Click the button "Power" and it will bring up a new dialog box. Look at the settings there. Set standby and hibernate to never then time it and see if it happens again.

Also boot into the BIOS, some BIOS will have a battery meter and this may shed some light on the issue. Let the system just sit and run in the BIOS for longer than it takes for them to shut down. This will help isolte the issue to hardware or software. If they shut down in the BIOS it is hardware, if they dont shut down in the BIOS it is software. To get into the BIOS, it will likely be the Delete key or F10. If all elese fails mash down on several keys till you get an error and then you should have the option to go into the BIOS.

Right click My Computer and select Manage, go to event viewer and look at the system log and application log. Look for errors, specifically system errors.

Start the system up in safe mode (F8) and see if it happens in safe mode.