Welcome to the forums!
Curious if the Windows Memory Diagnostic ran any better before you installed the additional memory, or try removing the additional memory to see if it's related.
Haven't tried it in awhile, but some people like using 'memtest' if you want to look into that.
Another idea is to just run it with one additional module at a time and in different slots if necessary to make sure it's not a bad module or a bad memory slot, but would like to compare with other kinds of memory if it's not too difficult.
Suggest you run Memtest Run it on your original memory, then 1 at a time with each of your new sticks, you need a good 6 hour run to insure good RAM unless you start getting error right away. This way eliminates any windows interference. Double check the spects of your new RAM Timings and Voltage must match, just having the same brand and model is not enough.
Memory diagnostics aren't able to catch all problems as far as I know, so would still like to find out if the memory you purchased will really work well with the G751JL although it sounds like you unit might have an unrelated issue as well.
Not sure if you're still under warranty and want to get that other problem checked out, but thinking there is a chance that memory you purchased may be incompatible if you have a way to return or exchange it (unless you have another G751JL unit lying around to compare with?).
Although we haven't approved the memory on our end, noticed there are some memory manufacturers that actually list memory they approved on their end for the ASUS G751JL if you want to go that route, but if you run into any problems, you will need to deal with them. It's possible they are assuming you don't have another memory module installed though and not sure if you want to go through the trouble of running your other memory without the preinstalled RAM.
For the blank screen issue connect an external monitor if you haven't already and try pressing FN+F8 to see if that will make any difference.
Anyway, you may want to get other opinions too since I'm not sure what is causing the problem(s) right now.