[Alienware m17x r4] Graphics Card & Power Issue

• 3rd generation Intel® Core™ i7-3740QM processor (6MB Cache, up to 3.7GHz w/Turbo Boost 2.0)
• 8GB Dual Channel DDR3 at 1600MHz (2DIMMS)
• 2GB GDDR5 NVIDIA® GeForce® GTX 675M
• 500GB 7,200 RPM SATA 3Gb/s

I had both these problems come out of nowhere starting yesterday.

1. GTX 675M not detected.
   1. Descrete graphics card: Not Detected (BIOS)
   2. GeForce Experience error when run
   3. Overall nothing related to the graphics card shows up anymore on my computer.
      1. Example: Right click on desktop, no longer a nVidia Setting Option

• Trouble turning on/restarting computer
  1. When I only have the power cord attached, the system gets power for just half a second then stays off
  2. When I put in the battery it has a small chance of turning on for a few seconds
  3. When I unplug the power cord and leave the battery in, it will do what I stated in b, then suddenly power on (randomly stays off)

I've never experienced these issues before, however it started yesterday when I noticed my Media Player Classic wouldn't play certain MKV Videos. I decided to restart the computer, however after pressing Restart the computer just shutdown and never turned on again by itself. At the time I only had the Power Cord plugged in.

I've been using my laptop like this for many many months, and I've had this laptop for 3 years. Nothing was changed with my set-up yesterday but somehow this happened. My power cord still shows the blue light so that shouldn't be an issue.

After that occurrence, even after I manage to turn on my computer everything is super laggy. Pressing the Start menu will kind of cause a stutter before it loads, my mouse cursor lags, I even get lag for opening folders. Also the area near the power button on my laptop seems to be really hot even when I have nothing open and remain on the desktop right after I turn it on.

What exactly is the issue with my laptop? I Googled and assumed that my Graphics Card randomly decided to die yesterday, however even if so... My computer performance shouldn't be affected so heavily? It's not like the GPU was used for opening normal folders... And I still have the Integrated Card.

Update: I also can't use any program that requires Direct X apparently, even though I still have my Integrated Graphics Card... So a lot of super basic games that should run on Integrated don't work either.