That's precisely the issue. Games never pop up a message that the memory's low. However, the system does slow down severely, to the point of freezing, and the game lags and lags, to the point of freezing, too. A check on task manager, then, shows a complete utilization of the RAM. Barring The Humbling Experience, which is surprisingly smooth for RPG, and games coded on Renpy, just about every RPG game lags. I've tried to play Road Trip and Elena's Life, for example, and I had to completely give up on the effort - they were just so unplayable. Anna - Exciting Affection, another game I happen to like, is barely playable, only after repeated "force closing" it.
That's the reason I want to upgrade. My system, as mentioned, is 32 bits, and it doesn't utilize more than 3 gigs of RAM. Upgrading to 64-bit, however, will allow me to add on RAM, too.
Anyways, everybody, thanks for the input. Considering it works, I'll definitely upgrade now.