Problems playing farmville/other games on my iMac

Hello, I just have a question. I tried asking on the farmville zynga forums but that was of no help at all.

I have been playing farmville for over 2 1/2 years now. Granted, it has always been glitchy, but anymore it just seems like it is almost impossible to play this game, sometimes it takes forever just to get the game to load, and even after it loads it is constantly freezing up. Frontierville is even worse, I have had to quit playing it because of these issues. As far as I know, my neighbors don't seem to be having these problems, or at least they aren't complaining about it. So basically, I just want to know... is the problem with zynga/facebook, my internet, or my computer?

My computer is an Apple, it has the snow leopard operating system, I bought it in 2007 but the hard drive crashed in January 2011 and was replaced with a brand new one. I have ATT DSL service, the speed is 3 mbps, I can't get the highspeed Uverse through them yet because it is not available in my area. Is my internet speed just too slow to play these games? I have tried different browsers, (and yes I am constantly "cleaning my cache") Opera and Firefox are completely unusable for these games, I bounce back and forth between Safari and Chrome, sometimes one works a little better than the other, but neither is great.

I have tried talking to Apple, but they don't want to say a whole lot without charging me, but they tend to blame my internet company/modem. ATT tends to blame the computer, but they did agree to send me a new modem. The new modem seemed to work for a little while, but now it is mostly the same old story. Its not like Farmville never works, sometimes it goes good for about 10-15 minutes, then the freezing up starts... its very frustrating and makes for a very unenjoyable experience...

So, I just would like a little advice... what should I do next? Should I pay the money to talk to Apple and have them look at my computer? Should I try to save the money, put everything on an external hard drive, wipe my computer clean, and try that? Or is the problem really just with these games.

Sorry that this was so long. I appreciate you taking the time to read this, thanks for any help that you can provide.