New memory installed. Strangely enough, the old memory was in slots 2 and 4—that is, in non-adjacent slots.
Which I found weird since I heard my computer likes memory modules to be installed in pairs. So with the knowledge that my computer has 2 sets of 2 slots, I expected two adjacent slots to be full and two adjacent slots to be empty.
I decided to trust the guys who put together my computer before I bought it and had Stella install the new memory in the remaining slots, 1 and 3.
Tried the Sims briefly; seemed a lot better, especially when visiting and coming back from other lots. Quitting the game was also a lot faster. Woohoo!