GPU Fan stops working after startup Alienware M17xR4

Model: Alienware M17xR4
OS: Windows 7 64-Bit
BIOS: InsydeH20 Version 03.72.24A12
GPU: AMD Radeon HD7970M, using Catalyst Control Center 14.2 Beta
CPU: Intel(R) Core(TM) i7-3820QM CPU @ 2.70GHz (8 CPUs) ~2.7GHz
RAM: 12GB

So recently my video card burned out for an unkown reason, but I was assuming just overusage. As a result I bought a new videocard, the same model (AMD Radeon HD7970M) and replaced the old one, keeping all other old components. When I booted it up, it worked as I hoped. I plugged in my second monitor and started up a game, but soon after, my laptop shut down and when I tried turning it back on, it gave me 6 beeps which I believe indicates GPU failure. After turning it back on again, I checked the GPU temperatures and they were at around 100 degrees celcius, and I understand my computer shuts itself down at around that temperature. I checked the fan by my GPU and it just isn't moving, and I’m guessing this is the problem. My CPU fan is just fine though. 
Here's a list of stuff I tried to fix this:
1. Reinstall video card drivers (wasn't sure if they were connected in some way)
2. Roll BIOS back to an older version (A09)
3. Update BIOS back to new version (A12)
4. Cleaned Registry using CCleaner
5. Physically cleaned my fan THOROUGHLY
6. Made sure everything was plugged in right, seems to be fine.
7. Checked power saving settings, all are on performance settings

Some quick notes while trying to fix this:
1. No software can detect that I even have a fan. GPU-Z says fan is N/A, as does HWINFO, MSI Afterburner, etc.
2. The fan by the GPU runs for about 5 seconds when I turn on the computer, and then stops spinning
3. When flashing my bios both times, the fan that seems to be malfunctioning runs at what seems to maximum speed until it finishes installing.
4. I'm not sure if the fan started doing this before or after my first video card burned out

I did read up a similar situation where someone took one of the wires and soldered it to the “+” side of the resistor, causing it to be on maximum as long as the laptop was on. Here’s the post as a reference. I’d only do this as a last resort. http://www.tomshardware.com/forum/65182-35-dell-m1530-stops-working-boot

I don’t want to send in my laptop to any tech support departments ideally.