What is the reason behind booting problem in ASUS X541U laptop?

The laptop may not boot up for a number of reasons. CMOS battery could be one reason.
Check if power light lights up or blinks. Check if you feel any vibration. Check the air vents if you feel air blowing. If you hear any beep sounds, note if it is short or long beep, single or double beep, etc.
Sometimes this helps - remove the battery, then press + hold the power on button for some more seconds.

Once you have some indication from above, you can google search that and fix it yourself if you are confident. If not call for professional help.

If there is simply no indication at all, and your power supply point (from wall) is working fine, then your motherboard is dead. Again you should be confident of your abilities to try to fix the MB yourself but this is not a simple matter. You need some specific tools and knowledge to do this part, and still you may not be successful in the end.

When you press the power button of your laptop then observe whether the power indication is there or not. If it is not there then it means that power is not coming to the laptop and then one has to check the mains chord and socket from where the power is being taken or check the battery if it is dead. One thing which can also be looked to is to remove the battery and try to run the laptop with the mains power only. From this we can infer about the status of battery also. These are the preliminaries and you might have seen all these basic things.

Next thing is remove or disconnect things like CD, USB device, memory card, internet cable etc from your laptop and try to boot it. If you have done some expansion recently like in memory card or hard drive then remove it also. Then again try for boot up. Sometimes CMOS reset is required. For that one has to disconnect it from mains (if it is connected) and then press the power button for 40 seconds which resets the CMOS. Again try to boot the laptop.

If your laptop power light is on it means everything is all right to the power adapter side or the battery if it is running on battery. But there is something wrong in the laptop. To check the screen functionality press Fn+F7 which would turn on and off any display on the screen. Adjust the brightness on the screen with Fn+F6 as sometimes faint intensity might mislead us. Next thing is you can try to connect to an external screen and by pressing Fn+F8 you can toggle between the two screens to ensure that your main screen is working all right. Of course this step requires an external display unit and connecting chord. Now repeat the earlier procedure of removing CD, extra memory card, internet connection and try to boot the system. If not successful just press the power button for 15 seconds and that would put off the laptop. (Note: These function codes can be different for different models so one has to find out it from the laptop manual).

If these primary things do not help then it would be better to go to the Asus site and find out the detailed procedure for the diagnostic and repair of the laptop.

Here are some workable ways to fix the booting issues in the ASUS laptop.
1. You can remove the battery and restart the laptop
There are various reasons that the laptop boots up abnormally. The simple way is to take out the battery and wait for some time and reinstall back and do a long press on the power button.
2. If any external device is attached, then remove it. Sometimes we found that removing external devices does the trick.
3. Repair Windows installation - One of the common reasons that laptop boot up abnormally is missing or damaged important files. You can repair windows by replacing these files and without changing anything else on the computer.
4. Windows Boot Genius can get your problem solved with easy steps.
5. You can visit https://www.asus.com/in/support/ to get online support services.
6. You can also reach to the ASUS service center - https://www.asus.com/in/support/service-center/india