You may want to buy another 4 gigabyte stick of ram and use it on its own to see if it still crashes to rule out the current one being ever so slightly bad that won't show up on memtest.
This probably won't fix the issue (memtest being designed to find memory errors) but the upside is you now have 8 gigabytes of ram which is much better for windows 10.
How full is your ssd?
is it running out of space or nearly so?
If the computer uses all of its ram and virtual memory, bad things can happen ... like memory degradation and crashes.
Since your cpu doesn't have an integrated gpu, the only way you can test another gpu is to buy another gpu ...
It doesn't have to be an expensive one, any old pci-e graphics card will do like this one:
I'd ask Best Buy before attempting this but they have a 15 day return policy for most items.
You may be able to buy the parts and test your computer then return the parts.
Do call and ask them first.
PNY - VERTO NVIDIA GeForce GT 710 2GB $47
http://www.bestbuy.com/site/pny-verto-nvidia-geforce-gt-710-2gb-ddr3-pci-express-2-0-graphics-card-black/5092306.p?skuId=5092306
If it runs perfectly with the above graphics card then we know your current gpu is bad.
If it still crashes then we have narrowed it down to either the power supply or motherboard(worst case).
A quick modeling of your build shows it should pull around 320 watts at maximum, a 500 watt psu
Cooler Master - Elite Power 550W
http://www.bestbuy.com/site/cooler-master-elite-power-550w-atx12v-2-3-power-supply-black/2268172.p?skuId=2268172
If the new power supply works fine then your current power supply is bad if not the issue can only lie with the motherboard.
The problem here is finding a store or site that sells LGA1156 motherboards
HP 8100 Elite MS-7557 LGA 1156 BTX $90
https://www.newegg.com/Product/Product.aspx?Item=9SIABGC4YW1714
This might be harder to return due to the size and weight of the motherboard incurring a shipping charge, both for buying and returning.
Disconnect everything from your current motherboard (/wrist) install the new motherboard and reconnect.
Due to a new motherboard you will most likely have to .... reinstall windows (/otherwrist).
The above was the long painful way to do it and assuming the issue isn't the motherboard and Best Buy honors your returns and fully refunds the money, will cost you little to no money, but a fair amount of time.
If the issue lies with the motherboard then the situation gets messy.
Of course you can avoid all of the above and go to a local computer repair shop to have them look at it.
They may charge you $100 to fix it and $50-$70 for the part that is broken, but they should have spare ram(which yours probably isn't bad), graphics cards, and power supplies to test with.
If the motherboard is bad they will have to buy one and charge you for it, but they will also put it back together and reinstall windows.
It's your call which method you want to use;
Test parts yourself with parts from Best Buy (Cheapest with biggest headache)
Bring the computer to a computer repair shop. (Expensive with headaches for the computer technicians)