Hello.
 
Thanks for the encouragement Slart.  Time to take the bull by the horns...
 
Gcruz...very interesting.  That seems to explain why Memtest finds no errors, yet the behavior is very much like a memory problem.
 
So it sounds like my next best step is to replace the memory, and when I do that to unplug and reseat all the electrical connections.
 
Sigh.  I appreciate everyone who offered suggestions on this.

EltonJohn
...I don't check on the temperature much, because the best way I know how to do this is in the BIOS, and I have to restart the computer to get to the BIOS...

Check what's on the disks that came with your motherboard. Some MBs include software for viewing BIOS
settings from within Windows.

Hello.  So I checked on the Intel web-site for the specifications of the i5-3570 processor, and their information is that this processor supports up to 32 gb of memory, and is compatible with DDR3-1333/1600 memory, and does not support ECC memory (funny - I thought all memory these days is ECC).
 
Here: http://ark.intel.com/compare/65702
 
So, I am not sure the memory speed per se is the problem.
 
But I do think my next best move is to replace the memory modules
 
Thanks again for all your thoughts and suggestions.
 
 

One additional possibility, not a freeze, but a USB issue, losing comms with the mouse and KB. Event Viewer is the place to start.

One other thing to try, if you haven't already done so is to clean and inspect the motherboard.  Dust build up might cause a component to overheat.  Inspect the electrolytic capacitors for leakage.  The tops should be flat and clean.  A slight bulge or leakage indicates a bad cap.  Good luck.