I'm gonna throw this xbox360?

So I'm really frustrated because it's my boyfriends nephew's birthday and we got him all of these games and he can't play them.
Now I'm pretty good with computers and consoles but this I just can't figure out.

They currently play minecraft, cod 4, and some ninja turtle game just fine. There hasn't been any problems they also rent games and never have any issues.
But we got them gta 5 and even cleared all of their memory unit memory (it won't let me access the hard drive) but it won't let me install because there isn't enough room.
So then we got him medal of honor warfighter (it has 2 discs) we're trying to use the multi-player disc but now it says we can't because his profile can't access live so that means he can't play.
Even though he can access live on every other game.
I've never had any issues like this with my xbox360
But this kind of sh*t is why I play pc. Haha

I'm a geek when it comes to technology lol but Grand Theft Auto 5 requires at least 7GB of memory. That's alot, are you sure your hard drive has enough space? GTA 5 also has downloadable packs that require some more space so your gonna have to make alot of room in your storage.

also there are many different reasons why his account can't access Xbox live. It could be that the internet connection is not getting a strong signal or the Ethernet cable is loose. But you say it only happens with medal of honor? It could be the game, not the console.