I used to be able to play my game+listen to music at the same time and if I wanted to run a second device for my game but ever since my sister and her boyfriend moved in and he plugged some blue chord (always forget the name of it) into the box thing for his computer and also uses the Internet on his Xbox which makes it impossible for my mum to even do her Internet banking. But my issue is that even when I take that chord out+no one is awake to be using the internet my game still has lag and that's just the game alone no music no second device. Anyone know what this problem might be?

Possible, that he set some bandwidth limitations to certain sockets of the router or even for certain users (if that's the box you're talking about). If you're not into computers much, I don't advise you to fool around with your router, instead tell your family about it and demand equal bandwidth for everyone, or a better service all together if it's not enough for everyone. If the guy moved in, he can pay a little bit more too if he's using more.
But if you know what you're doing, then just snoop around inside of the router's settings.