Are you sure it's a current model x51-R3?

Hopefully a Dell rep will soon post here what processors you can use on that motherboard.

I suggest you document your motherboard model, chipset, cpu socket type ... anything you can find.

I hope you are up for it because you are looking a quite a bit of work and expense. Some processor models might require the liquid cooler. Regardless of posted specs ... have you even tried to run Fallout-4 on this machine? What happens?

While i3-6100 is only a dual-core, it is quad-threaded (so, same 4 threads as some i5's).

Socket FCLGA1151 says this:

http://ark.intel.com/products/90729/Intel-Core-i3-6100-Processor-3M-Cache-3_70-GHz

But BIOS micro-code (to support various CPUs) might be limited since it's an OEM MB.

yea I'm positive its the current model... I know the model of the board is a rev a00 and chipset is the intel z170 at least I believe it is... I got the mobo number directely off the board and the chipset based on what it says its suppose to have Also yes I have fallout 4 on it right now and when I try to go into game it auto black screens then cuts back to steam...  Also how could I go about getting the cpu socket types...

Try CPU-Z to identify current hardware specs

http://www.cpuid.com/softwares/cpu-z.html

RE: Fallout 4

Like I said, looks like it will run on Intel-i3

https://www.youtube.com/watch?v=tl8HnV-Bqgw

Try searching Google. Have you tried Windows-8 Compatibility-Mode on Fallout-4 icon and/or Steam icon?

Here are just a couple of links

 https://steamcommunity.com/app/377160/discussions/0/496881136898292795/

or

http://www.pcgamesn.com/fallout-4/fallout-4-crashes-bugs-and-fixes

Just a guess, but I think your startup/crash is more or a general problem.

I got some answers for you, from Dell.

1. What Intel processors does Dell support on the x51-R3.
846P5, FY4X6 i3-6100,3.70GHz,3MB,65w
2JK73, GC0M7 i3-6098P,3.60GHz,3MB,65w
GXFK2, 37NHG i5-6402P,2.80GHz,6MB,65w
69J7M, 1GXR3 i5-6400,2.70GHz,6MB,65w
K80PX, J4CPH i7-6700,3.40GHz,8MB,65w
0D4GV, K991T i7-6700K,4.00GHz,8MB,95w

2. What AC-Adapters and Power-Boards are available for this model.
XM3C3 330w AC adapter
Y90RR 330w AC adapter
YHD64 Power-Board (Internal DC-DC Converter)

My Note: So, looks like x51-R3 only comes with 330watt Power-Supply ... good.

3. Which processors require only stock fan, and which require new low-profile liquid cooler?
* Undocumented. My guess, the 95w CPU would require the liquid cooler (or at least, a good idea).

4. Can liquid cooler be retro-fitted into an i3-based x51-R3?
* In theory, yes.