Camera keeps turning around?

One thing you can try. Turn the xbox on from the console itself. Once on, turn the controller on. Do not push any of the buttons or sticks while it is turning on. Start the game and see if that fixes your problems.

This first thing I would try to do is rule out either the controller or the console...

Is there anyone else you know with a Xbox 360 where you can either borrow one of their controllers to test on your system to see if the problem continues or to where you can take your controller to their Xbox to see if the issue happens there as well.

This way you will be able to at least rule out one or the other.  Narrowing it down a bit will help.

Like CubicleZombie said, it would be best to try and rule one of the two out. Do you have any other controllers that you could try and use while playing to see if you still have the problem? If you don't still have the problem then you will know it is your controller that is being faulty and that you will just have to use a different controller. Also, have you tried replacing the batteries in the controller? I am not sure if low batteries would cause that problem, but it is always worth a shot just to see if that would be what is causing the problem. Make sure to let us know what you figure out ect. and we will try to help you out as much as we can. :)

The problem has been there ever since I bought the console, so I think it's safe to rule low batteries out as the problemsource. I've tried to connnect all three of my old white controllers, but I've have yet to make them sync with the console (yeah, I have tried pressing the sync button on both the controllers and console at the same time).

I've tried connecting them to my friends Elite last week, and that didn't work either until we tried plugging them into the charger cable. As soon as they got plugged into that, they connected fine to the console and could be unplugged from the charger again.

So I don't know guys, my friend had the same connectivity problem, hence the reason he got those charger cables in the first place...

Well, if you tried connecting them to your friends Xbox and had the same exact problem - I would think the issue is the remotes.  The only reason I hesitate to stop there is that is seems like such an odd issue to present itself with so many remotes.  I would consider a call into support.