A high ping increases the load on your computer and you can lag with a great system if your ping is terrible. For example in L4D2, when my ping goes beyond a certain number, usually 400 ms, the game stutters and skips frames everywhere because it's not getting the information fast enough. I play with mobile broadband and although both are bad, the USB stick has a better ping rate than a wireless device. My normal is 100-120ms, which is bad but playable with online games. What's your ping?
If your internet's consistently bad enough to cause lag in every cut scene battle without exception then it might be difficult to ever play without issues online.