One final post on this, just in case it helps anybody out there. As I reported in my last post, I had narrowed down the problem to 2 particular DIMMs (when both are used at the same time). I ran Memtest for over 20 passes on each DIMM with no errors. I then used CPUID to obtain additional information on each DIMM. What I found curious is that although both DIMMs are branded Kingston, using CPUID one DIMM is identified as Kingston, but one DIMM is identified as Samsung. I had purchased both DIMMs at the same time (although I don't believe they were in a bundle), so I had assumed I was not mixing unlike DIMMs. Apparently I was wrong. Not sure if this is ultimately what's causing the problems (as the DIMMs had been working for several years without a problem, until recently), but I'm in contact with Kingston's tech support to see if they'll honor their lifetime warranty on the DIMMs.
Again, thanks for all of the help from this forum.