Aurora R4 video card upgrade from a nvidia GTX 680

10 to 30 percent upgrade to current is GTX1050 TI.

GIGABYTE GeForce GTX 1050 Ti DirectX 12 GV-N105TD5-4GD 4GB 128-Bit GDDR5 PCI Express 3.0 x16 ATX Video Cards-Newegg.com 

Can The $139 GTX 1050 Ti Outperform a $500 Graphics Card From 2012? - YouTube 

Hellblade Senua's Sacrifice GTX 1050 Ti vs. GTX 1060 vs. GTX 1070 vs. GTX 1080 - YouTube 

Since you have a 875w PS, I think a GTX-1070 or 1080 would work fine. You must be running the latest/final BIOS.

See this forum's recent Aurora video-card upgrade threads (there are several currently) and this (my recent adventure):

 Recommended NVIDIA graphics cards for Alienware Aurora R1 (2009 model) 

Your 16gb of Dual-Channel memory is nice.  As for speed, a bootable SSD as C: (around 256gb is fine) will make machine and Windows-7 faster than when new. Windows-10 (a free upgrade to you) is SSD aware and optimized.

As for your Aurora-R4 dropping dead (or developing a problem making it unstable or unreliable) ... it's possible , especially with a 5-year old machine. If you have been running it on a good UPS (like APC) it will likely live longer and stay trouble-free. Now-days, I recommend extended warranties. While newer machines (computers, appliances, cars, whatever) do seem to be more reliable, they are not immune to failure or design errors.

We now live in a "disposable society" and the new motto seems to be "less is more" or things only have to be built "good enough". There is a reason why some things are cheaper now-days. 

Edited

Thank you for the links. Much appreciated.

Yes there was some dust but not much and the fans were fine, which I did specifically check as I have noticed the system fan kicking off of late. And  I have always  tried to keep my PCt dust free because that can make the temperatures go up. It is normally about 1180 rpm but it's been  going up to 1200-1350rpm in game and historically it never used to. So something's not quite right. I just need to do some more investigating and yes I have kept up the warranty on  this machine. You could say it's running warmer in the summer, but a couple of years ago  it was 31 degrees ambient temperature before I even played a game and the fans didn't kick off l like they have been of late. I have the thermal controller in my toolbar now because I'm  getting paranoid about it. :/

I got my first BSOD about a month ago but reseating the card seemed to fix it

It's good you looked into and fixed this already. Some people just let it go or think a new video card (always looking for an easy fix) will fix it. What they end-up with is a flaky machine with a new video card. 

Hopefully, while you were in there you cleaned all the dust out (air compressor at 40psi works nice) and verified all the fans are working. Also inspect and possibly re-seat the vital plugs and connections.

Fizzgigg wrote:

Yes there was some dust but not much and the fans were fine, which I did specifically check as I have noticed the system fan kicking off of late. 

Like your outdoor HVAC unit, the radiator fins must be dust-free for optimal heat dissipation and optimal performance. Use air-compressor, blowing from inside to outside first, then the other way.

After this much time, the thermal-paste between the CPU chip and heat-sink ... might be drying-up and not transferring heat as optimally as before.

After those 2 things are done, if still not working acceptably ... after many years, some of these "sealed system Asetek liquid-coolers" eventually start to get clogged-up with coolant residue.