I found the problem, failing memory (RAM). I had to go through the following rigamorole:
I tested the memory using Mem86+ and it tested bad.
I tried reseating the RAM sticks, switching sockets, running just 1 stick (4 GB) at a time. One of the sticks tests good, the other bad. I looked on the G.Skill (RAM manufacturer) support page and found a notice to AMD users to manually adjust the DRAM settings in the BIOS (what a PITA). I looked in the BIOS and the auto settings were wrong (the rated settings are 9-9-9-24, 1.5 Volt, 1600MHZ, the BIOS had 11-11-11-28, 1600MHZ. I further read that the most stable setting is 1333MHZ, 1.5 Volt, 8-8-8-24, which is what I set it to.
I ran the memory test for over 6 hours on the 'bad' RAM stick, in the 7th pass and still no errors when I stopped the test, it never got past the second pass without errors before I changed the settings. I thought everything was OK so I put both RAM sticks in and ran Mem86+ again. It took a long time but the RAM failed the test. I reseated the memory and ran it again just to be sure and it failed again.
It looks like the RAM kit is bad and I have to return it for replacement (G.Skill has a lifetime warranty).