15 R4, battery replacement, #5

Dell shows two batteries for that laptop.

Parts-People also shows two types, though they are currently out of stock.

It's good that you caught it.  A swelling battery can damage components such as touchpad and keyboard.

Please do not throw it in the garbage. Take it somewhere that it will be properly disposed of. In many places, stores such as Best Buy and Staples will accept old "tech" for proper disposal/recycling. A recycling depot may also accept batteries.

These links should be helpful to you:

Swollen Battery Information and Guidance | Dell Canada

How Do I Recycle or Dispose of My Dell Battery | Dell US

Whenever touching components or working inside a computer, wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. It's a cheap and sensible precaution. Rest the laptop on an anti-static mat or at least a reasonable alternative such as corrugated cardboard. (Repeatedly touching a metal case part is not sufficient mitigation with modern components.)

Hi @doominator welcome to this free user-to-user Alienware laptop discussion forum. 

The purchase of a Genuine OEM Alienware 15 R4 battery is getting more difficult. Please use the additional purchase protection from Amazon, eBay, Parts-People. The Dell laptop has a self-protection circuit that prevents a dubious battery from being charged or accepted. Getting a Genuine OEM Alienware battery may seem expensive when compared to a battery that is not Genuine OEM, but that can be false economy. The new replacement battery shall have a white label with the correct Dell Part Number (DP/N), look beneath the QR square matrix at year/month date, which should be less than six months old. 

Genuine OEM Alienware 15 R4 battery 99Wh is DP/N 9NJM1 

Genuine OEM Alienware 15 R4 battery 68Wh is DP/N 44T2R 

Consult the Alienware 15 R4 Service Manual for Removing the battery or Replacing the battery.