This could mean the PC bios is not correctly obeying ACPI power management instructions. There could be two main reasons for this - first Windows was originally installed without the bios acpi choice being correctly set, and secondly the bios might be out-of-date.
In the first case, there is no option other than reinstall windows. In the second case, you can re-flash with a later bios from the motherboard m/f site. I do not recommend either if you are not a fairy experienced PC person.
As a simple effort to make some difference, you could open the power options in control panel, do whatever you can to disable all power monitoring (i.e. disable hibernation, set all monitor, HDD, system standbye to 'never'. Then reboot. See if the PC now behaves normally as regards shutting down from the start button.
If this affects a cure, then probably acpi is correct, and you could re-enable any power-saving settings you wish. If it makes no difference, the acpi setting/bios problem is the likely reason.