The memory problems may certainly be contributing to your trouble with COD2, but there is another possibility... COD2 doesn't like AMD X2 processors. Don't worry, there's a solution: "ROPE" (Run On Processor Explicitly) is a small application to force a program to run on just one of the processors in a multi-processor setup. You can download it here:
It's very easy to use, just alter the 'Target' in COD2's shortcut to (include the quotes, and I'm assuming the paths below are correct for your setup):
"C:Program FilesROPEROPE.exe" -f 0 -n "C:Program FilesCall of Duty 2cod2sp_s.exe"
Hope this helps. It certainly cured ALL of the problems I was having with COD2 on my system.