So looking online at system spec requirements it is a pretty simple game. 2.3GHz processor (assuming single core), 1GB of RAM, 100MB drive space.
That said, from what I can tell it is largely flash based, and even the log-in page crashed both IE and FireFox... so we are not exactly talking about a game that is optimized or well written. My guess is that your old Core2Duo is the cause of any lag as it just barely eeks over the 2.3GHz requirement. Also, systems that old tend to only have 1-2GB of RAM by default, which means that you probably don't have a full 1GB of ram to dedicate to this game (windows and a web browser alone will eat 4GB).
So here is the rub:
1) adding a GPU will not help with this game, plus being a mini-tower you...