When complete shutdowns with no warning, errors or freezes happen, it usually has one suspect.
Power Supply.
By the look of your specs, you must have a very low tier 500Watt. After you upgrade the CPU, its now possibly tripping it.
Beware, the 65Watt TDP you mention, is not the actual power draw.
I don't want to push you into a brand new PSU purchase but by the looks of it, you may need it. Another thing that i can tell you, an A320 board is not really the best thing in the world for a ZEN4 CPU but it should work.
Try to disable core performance boost, this makes the CPU use less energy, maybe it will help.
Good Luck
The Englishman