Apple Thunderbolt display not turning on when connected to ASUS Z87 motherboard
Okay, I have figured it out myself :)
Feeling extremely happy.

Steps:  


Enter BIOS setting. For most of the computer, you just have to press
F2 while computer starts.
Enter Advance BIOS setting mode.
Enable iGPU and Multi-Monitor option in the Graphics section.


That's it. Restart your computer and Enjoy the terrific Apple thunderbolt display quality in Windows operating system.

My PC specs:


Motherboard: ASUS Z87 Expert
CPU: Intel Core i7 4790k
Discrete GPU: Sapphire R9 270X 2GB Dedicated
and Apple Thunderbolt Display 27" :)


Any Windows operating System (7/8/8.1) will work but my my operating system is Windows 10 Technical Preview.

Here is a screenshot