Memtest - Instructions:
Download the ISO (or the .exe for pendrives) from here Memtest86+ - Advanced Memory Diagnostic Tool
Then (if you have chosen the ISO) burn the ISO using ImgBurn: The Official ImgBurn Website
Boot from the CD/USB and run the test (at least 5 passes per test) with only one stick of RAM in place, if the stick passes then swap it into the other sockets in turn until you can be sure that all the sockets are fine.
Then test the rest of the RAM one at a time (no need to swap the sockets; still 5 passes per test).
It is a time consuming process but it is the only way to be sure it isn't a RAM fault.
For your final test, run the test with all the RAM in place.