I was finally able to install Linux on my Alienware 14, after a fierce battle!
A few things:
My laptop came with Windows 7 installed in LEGACY mode with SECURE BOOT OFF.
The Linux version I was able to get to work is Linux Mint MATE 64 bit, the Cinnamon version wouldn't work with this laptop.
I had to use a USB wifi adapter to connect to the Internet during the install, the Broadcom 4352 based internal wifi wasn't recognized by the live CD, I bought the USB wifi at newegg.com, the webpage is here: http://www.newegg.com/Product/Product.aspx?Item=N82E16833166068
Step 1: Resizing your drive and creating the necessary partitions:
Download the iso and burning it to DVD, here's the iso: http://www.linuxmint.com/download.php
Boot to the DVD by pressing F12 when the you see the F12 choice, use the down arrow to select CD and press "enter"
When the live CD menu comes on the screen select COMPATIBILITY MODE, and press "enter"
Once the desktop comes up, press the MENU button,(bottom left) and select "SOFTWARE MANAGER". In the upper right corner of the Software Manager,(search box), type in Gparted and hit the hourglass. Install it.
Select MENU>ADMINISTRATION>GPARTED to start the partition manager once installed.
On the top right corner of the Gparted is where you select the hard drive you want to change the partition on, if you haven't added a second hard drive it will be /dev/sda.
You will see that the hard drive has 3 partitions on it, sda1, sda2, and sda3. DO NOT TOUCH sda1 or sda2, or you can really screw thing up!! You should really make a disc image of your hard drive before you go any further!! There, you've been warned!!!!
Select the SDA3 partition by left clicking on it, once, to select it, then right click it and select resize/move. Select the right side of the white graphic and drag it to the left, to shrink the Windows installation to make room for the new partition you're going to create. Shrink the Windows partition as much as you want, it's totally up to you how much room you want to leave for Windows, I left 200G on my install. Now, with the freed up unallocated space on the right, right click on it and select "NEW". Select "create as EXTENDED" partition. Next, right click on the new EXTENDED partition and select NEW, "create as LOGICAL" partition. This will be for your swap partition. Drag the left side of the graphic to the right and make it approx. 8G. You may be able to use a smaller one, but I thought 8 was good. When you're done the right arrow on the graphic will be all the way to the right, and the left arrow will be 8G from the right. You can also use the number rows by putting 0 in the "Free space following MIB", "New size MIB" 8000, and the balance of the drive size will be in the "Free space preceding MIB". Select "linux-swap" in the "File system" row. Leave the "Align to"
row as MIB, and type in a LABEL if you want one. It's easier to identify your partitions in the file manager if you use labels. This will create the swap partition at the end of the drive. Click on ADD.
Now we'll create a logical drive for your linux install. Right click on the unallocated space, select NEW , then select the right side of the white graphic and drag it to the left, making as much space as you want for your Linux install I used 50G for my install, probably WAY more than I need. If using the numbers you would type in 0 in the "Free space preceding MIB" row, 50000 in the "new size" row, and the balance of the drive will be in the "Free space following" row. Click on ADD.
At this point no changes have been made to your drive, if you are happy with what you have and want to make changes to your drive, click on the arrow with the 90* bend to the left on it, just above the main graphic, it's the far right arrow, and wait, this will take awhile. The other arrow is the undo arrow.
If things went correctly, your hard drive will now have the original partitions sda1, sda2, sda3, possibly a small unallocated space, then sda4(extended partition), sda5,(swap partition), and sda6,(your soon to be MINT install). If the numbers aren't correct, that's not a problem, what's important is that you have your original 3 partitions and 3 more that you created.
Step 2: Installing MINT
If you have a USB wifi adapter place this in a USB slot, put the Mint MATE live DVD in the drive, reboot and press F12 when the option shows.
At the Mint menu select compatibility mode. When you get to the desktop, double click on the INSTALL icon. Select English for your language and keyboard, unless you are/have something else. When you get to the screen with your hard drive partitions, select CHANGE, select,(left click) the 50G partition,(or whatever size you created). It will probably be sda6, it will be the bigger one of the 2 that you created. Format to ext4, mount point /, create bootloader in sda3. You don't have to do anything more to the swap partition. When it's done the screen will show sda6 having the / . Click ok to continue. At some point it will ask you to create a username and a password, remember it! Select the log in automatically, and no encryption, unless you really need it. After this, just follow the directions. and finally it will ask you to remove the DVD and press enter to reboot. When you reboot you will see the GRUB boot menu, select Linux Mint, the FIRST choice NOT the compatibility mode. You will finally come to your desktop, if you still have your USB wifi connected, you will be able to connect to your wireless network, if not, you won't be able to connect. I couldn't get the internal wifi to connect.
Step 3: Getting your internal wifi to work.
I bought the Alienware 14 with the Broadcom 4352 wifi chip in it, if you have the "Killer" internal wifi you may or may not have to do this.
In order to get my internal wifi to connect, I had to install the latest Linux Kernel. Here's the website with the directions. http://ubuntuhandbook.org/index.php/2013/12/kernel-3-12-4-install-upgrade-ubuntu-linux/
After following the 64 bit directions, reboot.
Now you have to install the driver. Go to MENU>ADMINISTRATION>DRIVER MANAGER. Click on the Broadcom driver and click ok. It will load the Broadcom driver for you. If you have the "Killer" wifi, I assume it's driver will show up here, do the same thing to that one.
That's it, ENJOY! If you have any questions, leave a message here, or email me and I'll do what I can to help. I've installed Linux on many laptops and desktops and this, by far, was the most difficult install I've found to date. Hopefully I didn't leave any steps out, but if you need help, just ask. The guys in the forums at http://forums.linuxmint.com/ are very helpful too.
Are you trying to install Mint 16 MATE? That's the one that worked for me. If so, you have to start the LIVE CD in compatibility mode to install it, then once installed it worked without any more work on the system.
Are you using MATE? Are you installing on an Alienware 14? I installed it a couple times this way and it went great, the only thing I had problems with was the wifi working. I laid that out in the guide I wrote.