There's no way your laptop affects the performance of your newly built computer, however. Besides, any decent store should replace your hardware if it's faulty, even I had no problem replacing a defective RAM stick.
Oh, and the only reason to want 60+ frames in your games is your ego. Thanks to synchronization, more FPS may not always be better, and you would almost certainly be unable to notice any difference between different high framerates. Of course, if you have a game drop to 10 FPS from 30, you have a problem. But if you're running a game at 60 FPS and it drops down to 40 for a while, you don't have a problem.