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

Is this latest firmware update the Alienware m15/m17 R2 System BIOS | Driver Details | Dell US (currently system BIOS Version 1.18.3).

Installation of incomplete BIOS file can prevent the laptop booting into the operating system. If Alienware splash screen F12 boot menu available, use BIOS Flash Update option. How to flash the BIOS on a Dell Desktop or Notebook with a USB thumb drive | Dell US. 

I've never heard of a failed BIOS update causing a short. Does the power adapter light turn off when it's plugged into the system? If it does, then you have a short on the motherboard. A bad BIOS flash can sometimes result in the laptop having no signs of life though, this is usually due to the BIOS chip being too corrupted to allow POST. It's possible that replacing the BIOS chip can fix it but you may need to replace the board. 

Yes on the power supply light. If I unplug the power supply, the light that had been off comes back on. When I go to plug it into the laptop, the light immediately goes out.

My laptop was working fine today before the firmware update. It really seems like the update ruined my laptop.

Is there anything I can do? 

Unfortunately that usually means that the system board is shorted. Other than replacing the board there isn't much you can do. If you take it into a good PC repair store then they may be able to trace the source of the short and replace the bad component(s) but it isn't always easy and they'd probably need a board schematic. 

There's a slim chance that the DC power jack is the problem but it's almost always something else on the board. 

Hi @Lurky McStab thank you for sharing additional information.

The ac adapter (charger) and/or Power-adapter port can be replaced. OEM Alienware m17 R2 DC Power Input Jack Plug with Cable is DP/N J60G1. 

Man, it would be amazing if that was the issue, rather than having to replace the motherboard. Thank you! (BTW, do you have the part number for the motherboard, just n case?)

Hi @Lurky McStab thank for sharing update. 

You may wish to contact $100 Dell Laptop Repair | Dell Repair | Laptop Repair | Notebook Service Center (parts-people.com). They will first diagnose your laptop's problem and contact you with your options. They will always attempt to repair your existing parts before just replacing them, but if you do need parts replaced, they might have them in stock. 

Please share which Alienware m17 R2 option of system board (aka motherboard) was purchased, see list of CPU & GPU Processor specifications. Thank you.