Alienware M17 R3, Plugged In, Not Charging

Question:

How do I get my laptop to not just maintain its current charge but furthermore actually charge up to 100% available battery, with the current issue of "Plugged In, Not Charging"?

Background:

I have an Alienware M17 R3 that I've had for 2 years now and just recently my charger died (when I would have it fully plugged in, my laptop wouldn't recognise it and furthermore the light would not come on the charger indicating it was on), so I decided it was about time to just get a new one. I ordered a new one and three days later it shows up and I eagerly plug it in only to find that I get the message now of "Plugged In, Not Charging. This means it will maintain the charge it is at, and won't progress downwards (even if on High Performance and playing a game, or go upwards (if I leave it on Power Saver overnight). I do not believe it is the battery because the battery still indicates that it is not only at 57% original capacity, but most notably it was not an issue before my old charger died and thus I conclude it is not the battery.

Things I have tried:

1. Plugging in and unplugging all pieces of the charger and plugging it into different electrical outlets (Oh, and there is a light on the charger that indicates it is 'on', and that is in fact indicating that it is on).
2. Updating BIOS won't work because I had less than 10% battery, furthermore the latest version for my laptop is 'A12', and I checked the BIOS information and it was in fact version A12.
3. Shutting down. Unplugging the charger from the laptop. Taking out the battery. Holding the power button on the laptop for more than 30 seconds. Putting the battery in. Plugging back in the laptop. Waiting 30 seconds before turning the laptop back on. Turning it on, and still having the same problem.
4. Doing the above except also uninstalling the Microsoft ACPI-Compliant Control Method.
5. Allowing for a full discharge of the battery (Yes, as of writing I am currently at 0% battery).
6. Shutting down. Unplugging charger. Taking out the battery. Plugging in charger and starting the computer up. Letting the laptop run on just charger electricity works/sustainable, however effectively converts it into a desktop, and I don't feel this is a viable permanent state because I paid $1800 for a laptop, and not a desktop.
7. And finally, atleast of the things I remember trying yesterday; wiping my hard drive and sparing no single file or driver. I have wanted to do this anyways since it has been awhile since I have. Nonetheless, still have the problem.

Things I have concluded that could be wrong but I think are right:

1. It's not the charger itself.
2. It's not the battery itself.
3. It should not be any software preventing it from working.
4. Truly, I believe it has to have some sort of connection between how the electricity from the charger goes from the charger to the battery, in a communicative way.
5. I base this off important facts such as: No problems before I had to replace my old charger, and the ability of the laptop to work without a battery but nonetheless still plugged into the new charger.

Anyways, I'd appreciate any help that anyone could offer me, and I thought I would post a new thread for this because others that I have looked at had the solutions in which I have outlined yet do not work for me, and sometimes do not work for those people. Willing to provide anymore information that shall help in the 'fixing' of my laptop. Thanks!