Thanks for your reply!

I didn't notice an on board GPU, however I may have missed it. I'll work through these steps you've outlined nicely for me when I get home from work.

When I start the pc without the crossfire or the older GPU I was using it does 5 beeps and a pause, repeat. No beeps with the crossfire installed. There is one medium to fast speed blue light blinking on the MIO board. Along with a steady orange light. 

Thanks for the reply, speedstep but I am not having trouble with the pc shutting down.

Does the R4 have on-board video?  If so, take the video card out and plug the monitor into the back of the motherboard's video output.  If you get a picture there, then there's probably an issue with the discrete GPU getting power.

Edit: I realize you're talking about card(s) - plural.  Then you mentioned crossfire.  You also said that the cards work in another machine.  If so, then it's not the cards. It's possible that the PSU has gotten old and can't supply enough power to both GPUs at the same time. Try plugging in only 1 video card then turning the PC on.  If that doesn't work, turn the PC off and swap the card with the other one and repeat.  If you do get video, then you know one of the cards is borked.

If still no video, try to isolate the issue.  Leave one card in and remove all memory modules except for one.  Keep swapping RAM sticks out until the computer boots.  If it boots with one, shut it down and add another.  Keep trying until you've found out if it's a bad RAM module.

When it powers on but no video, do you notice any flashing lights or beeps coming out of the PC?

Not sure about the lights, but 5 beeps in a Dell desktop signifies an issue with RTC or real-time-clock.  Some people have solved the issue by simply replacing the CMOS backup battery on the motherboard.

Then again, others have done so and it still beeps 5 times so it's really a toss up what those 5 beeps could actually mean.  What it is telling me though is that something is borking up your R4's normal boot routine and it's halting as a result.

If it was working before but then suddenly quit, there's a whole lot of things that could have gone belly up.  Old capacitors in the PSU failing so voltage fluctuations causing instability to bad RAM, or even clogged AIO pumps causing the processor to heat spike and shut down.  Who knows?  Best thing to do would be to engage in a process of elimination.  You already know those crossfire cards work so start looking at something else in the system and eliminate components until you find the source.

Oh and not sure if you've already tried, but if not, clear the CMOS.  Leave unplugged, pull the coin cell battery and let it sit.  Depending on your motherboard, you might have to fiddle with a jumper as well.  

Sorry to hear about your loss. I don’t have an R4 so it’s hard to help out here. Anyway, here’s a link about the blinking on the MIO

https://www.dell.com/community/Alienware-General-Read-Only/Alienware-Aurora-R4-MIO-Board-Light-Blinking/td-p/5539159

You may want to check out the Alienowners website where there could be more R4 owners that can help.

Hello all, thank you for your replies! 

I've made some progress. I tested out the RAM with the process of elimination. Found no issues. Tried having just one of the two crossfire cards plugged in, also nothing. I checked for an on board gfx, don't see one. I also do not see one of those nickle shaped batteries on the motherboard?

I have had one success. The blinking blue light in the MIO was due to bad rechargeable batteries. Replaced them, solid blue light now

 From what I can tell through reading all of your replies, I'm in for a new PSU. I'll give this a shot and see how it goes. 

Note, looks like you have to remove the GPUs to see it. 

Your PC does't come with onboard graphics.  But since the problem occurred when you were adjusting the GPU settings, and the PC works fine with a different GPU (and on the flip side the crossfire GPUs work fine in a different system), I'm not sure that the issue is with your power supply.  Before replacing that, I'd first suggest completely uninstalling the drivers and any software for the amd GPUs and then reinstalling clean.

I also do not see one of those nickle shaped batteries on the motherboard?

If you look at the user manual in the link below:

https://downloads.dell.com/manuals/all-products/esuprt_desktop/esuprt_alienware_dsk/alienware-aurora-r4_owner%27s%20manual_en-us.pdf

On page 20, isn't #12 supposed to be a battery? Do you not see that on your R4's motherboard?