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

Laptop without battery is designed to function as Desktop on ac adapter (charger) power. 

Is this POST (Power On Self Test) diagnostic notification real, or a false positive? Re-paste and clean will not fix 2,1 Processor failure, which could also be motherboard power rail failure. CPU and GPU are soldered onto motherboard. 

Does system boot provide Alienware logo splash screen with F2 and F12 options. If yes, when splash screen appears, press and hold down F12 key to enter boot menu. Use up and down keys to find Diagnostics option and press Enable to run ePSA diagnostics. How to Run Dell ePSA | Dell SupportAssist On-board Diagnostics (Official Dell Tech Support) - YouTube. 

If not recent Dell purchase, Dell Warranty and Service Extension - Dell Community  will probably say "Your device has reached the end of service life and can no longer be renewed, upgraded, or extended."  

If 2,1 Processor failure notification is real, you should explore if you want to repair or get new/refurbished PC (same specification Desktops are cheaper than Laptops). 

How to Arrange an Out of Warranty Repair on Your Dell Computer | Dell US 

$100 Dell Laptop Repair | Dell Repair | Laptop Repair | Notebook Service Center (parts-people.com) 

Dell Alienware 17 R4 Laptop Replacement Parts | Parts-People.com 

Refurbished & Overstock Laptops, PCs, Monitors: Dell Outlet | Dell USA | Dell USA 

Dell Outlet Search Results for Alienware | Dell USA

Try removing the CMOS battery for 15 minutes then reinstall. This forum post also touches on that problem and MB replacement may be needed. That MB can be found at Parts-People here.

Hi @vadyma please post update on what fix (if any) works for you.