why Ubuntu is not working on my Alienware M14X laptop computer?

Try booting the installer with the nomodeset boot option (see http://ubuntuforums.org/showthread.php?t=1613132). If that works, then you can make it permanent for the installed system and/or install different video drivers (e.g., you could install the proprietary NVidia drivers in Additional Drivers or by manually installing the nvidia-current package, once the system is installed). The best ultimate solution (in terms of whether or not to use nomodeset and what drivers to use) will involve a combination of what works at all, your personal preferences, possible non-technical considerations (perhaps you are averse to running non-free software and thus might not want to use the proprietary drivers), and what yields the best performance.

If you successfully provide the nomodeset boot option but it still does not boot, then:

Did you MD5 test the .iso image before you burned it to CD/DVD or wrote it to the USB flash drive? (See https://help.ubuntu.com/community/HowToMD5SUM.) If not, please do that now. If that doesn't check out, you'll have to redownload the .iso image, MD5 test the new image, and (assuming the new one checks out) burn a new disc or write it to the USB flash drive again.

Did you verify that the live CD/DVD/USB was written correctly and is readable by the machine on which you're installing? To do that, boot from it, and immediately when you see the person and keyboard icons at the bottom center of the screen, press Spacebar, select your language, and select "Check disc for defects". (This goes for USB flash drives as well as CD's and DVD's.) If that doesn't check out, you'll have to burn a new disc or re-write the .iso image to the USB flash drive (and run this test on it again).

If the above enables you to solve your problem, then you can mark this question as Solved (you can do this at https://answers.launchpad.net/ubuntu/+question/167278). Otherwise, in your reply, please include a detailed description of the "screen issue" you are experiencing, as this could be many different things.