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

Dell has a protection system to prevent their laptops being damaged by battery and/or ac adapter. Are you sure that these chips have failed? Was Alienware x17 R1 laptop purchased with a Dell warranty? $100 Dell Laptop Repair | Dell Repair | Laptop Repair | Notebook Service Center (parts-people.com) 

Hi. Warranty expired in July of this year, haven't renewed it. A technician-friend tested the chip and found it no longer working.

Hi @JintuDesigns thank you for the clarification.

A MOSFET usually has three terminals and can be bolted to a heatsink, Testing a MOSFET – How to Conduct an Effective Test (wellpcb.com). 

The image in the opening post appears to show two 8-pin dual in-line package designated EML 1114, within red circle. 

I have been searching for EML1114 to no avail. I also do not have any idea if there are compatible chips out there.

Those are "SMT" (Surface Mount Technology) components.   Even if you found replacements, special SMT desoldering and soldering equipment is needed.  Does your tech have the specialized tools?

It would be best to contact the linked Parts-People for repair.

He has all the tools. Only the eml1114 is hard to find.

I also have issues with the mosfet on x17r1. mine was refurbished by dell and the chips on mine are DMP32M6SPS. One was shorted gate to drain.  I got 2 at mouser.com. As long as the specs for the mosfet are the same for your chips those should work fine. I haven't installed mine yet, should get my lead-free low heat solder paste today.

So the $2.02 mosfet from mouser.com works just fine! Saved the $50.00 diagnostic fee plus whatever Dell depot repair would have charged for replacing it. The old one just popped off the board with hardly no pressure, showed what appeared to be very bad solder on the bottom (drain) and a small part of corner for the pad gone, probably from the time they refurbished it.