If you have a Realtek Network Adapter, the problem might be the Microsoft driver that is updated along with the operating system, replacing your network driver that worked fine when you needed to wake your computer after a normal shutdown. So you just need to update the network driver to the latest version that is available for download on Realtek website.
Download link for Realtek Latest Network Drivers: realtek.com.tw
Then you need to set Shutdown Wake-On-Lan to be Enabled and restart your computer.
We assume that BIOS settings are correct and Wake-On-Lan for PCI devices is enabled, and the rest of windows settings are all correct.
If it still does not work do this:
Step 1: Open the Power Option item in control panel.
Step 2: Click the Choose what the power buttons do link.
Step 3: Click Change settings that are currently unavailable.
Step 4: Clear the Turn on fast startup(recommend) check box.
Step 5: Click Save changes.